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Play With Geometry

Master class 6 to 10 Geometry while playing with it

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All 360 Play With Geometry lessons

Every lesson in the series, by class. Every lesson is free to play once you sign in.

Class 6

  • The Tiny Dot — A mark of position with no size · Fundamental Concepts
  • The Infinite Line — Stretching forever in both directions · Fundamental Concepts
  • The Line Segment — Connecting two points with the shortest path · Fundamental Concepts
  • The Ray's Journey — One fixed start, infinite direction · Fundamental Concepts
  • The Infinite Flat Surface — Length and width, but no thickness · Fundamental Concepts
  • Open vs. Closed — Where do the lines meet? · Fundamental Concepts
  • The Perfect Cross — meeting at exactly 90 degrees · Fundamental Concepts
  • Perpendicular Bisector — always at right angles, exactly in the center · Fundamental Concepts
  • Collinear Points — When three points share one straight path · Fundamental Concepts
  • Parallel Lines — Lines that never meet · Fundamental Concepts
  • When Lines Cross — Discovering the single point where two lines meet · Fundamental Concepts
  • The Meeting Point — When lines cross at one spot · Fundamental Concepts
  • Supplementary Angles — adjacent angles always add up to 180° · Fundamental Concepts
  • The Angle's Birth — where two rays meet at a vertex · Fundamental Concepts
  • The Degree Spin — spinning full circles into 360° · Fundamental Concepts
  • Angle Classifiers — acute, right, obtuse, straight & reflex · Fundamental Concepts
  • Angles Around a Point — The sum is always 360° · Fundamental Concepts
  • The Adjacent Angle Rule — sharing a vertex, an arm, and opposite sides · Fundamental Concepts
  • The Crossing Lines — vertically opposite angles are always equal · Fundamental Concepts
  • Congruent Angles — Same measure, same shape · Fundamental Concepts
  • The 90-Degree Match — Two angles that complete each other · Fundamental Concepts
  • Supplementary Angles — Supplementary angles on a straight line · Fundamental Concepts
  • The Triangle's Definition — Three sides, one closed figure · Triangles
  • Where Sides Meet — Discover the vertices of a triangle · Triangles
  • The Triangle's Secret Sum — Why interior angles always add to 180° · Triangles
  • The Exterior Angle Secret — always equals the sum of the two opposite insides · Triangles
  • The Acute Triangle — When every angle stays under 90° · Triangles
  • The Obtuse Triangle — When one angle steals the show · Triangles
  • The Right-Angled Triangle — Meet the hypotenuse & the 90° corner · Triangles
  • The 60° Secret — Why equilateral triangles always hide three equal angles · Triangles
  • The Isosceles Balance — equal sides always hide equal angles · Triangles
  • The Scalene Triangle — three sides, three different lengths · Triangles
  • The Altitude's Path — meeting at the orthocentre · Triangles
  • The Median's Meeting Point — Where three lines converge · Triangles
  • Four-Sided Figures — Defining the quadrilateral family · Quadrilaterals
  • The Quadrilateral's Secret — Why four corners always add up to 360° · Quadrilaterals
  • Parallelogram — opposite sides always stay parallel · Quadrilaterals
  • The Four Right Angles — What makes a rectangle, a rectangle? · Quadrilaterals
  • The Rhombus Rule — four equal sides, one special shape · Quadrilaterals
  • The Square's Signature — four equal sides, four perfect corners · Quadrilaterals
  • Trapezium — exactly one pair of parallel sides · Quadrilaterals
  • The Parallelogram's Secrets — opposite sides equal, diagonals bisect · Quadrilaterals
  • The Circle's Secret — One center, one distance, endless points · Circles
  • The Radius Rule — always equal, always from centre to edge · Circles
  • The Diameter's Path — Always through the center, always double the radius · Circles
  • The Chord Connection — joining any two points on the circle · Circles
  • Secants & Tangents — Two lines, one circle, infinite possibilities · Circles
  • Arcs of a Circle — Minor vs Major: The Circle's Split · Circles
  • The Pizza Slice of Geometry — Exploring the magic of sectors · Circles
  • Circle Slices — Discover segments, minor & major parts · Circles
  • Inside, On, or Outside? — Exploring the regions of a circle · Circles
  • The Mirror Line — Discovering the Line of Symmetry · Symmetry
  • The Circle's Infinite Mirrors — Every line through the centre is a line of symmetry · Symmetry
  • Folding Triangles — Finding lines of symmetry in triangles · Symmetry
  • Symmetric Point — where every point finds its twin · Symmetry
  • The Angle Twin — Copy any angle perfectly every time · Constructions
  • The Angle Splitter — cutting any angle perfectly in half · Constructions
  • The 60° Blueprint — Building perfect angles with compass & ruler · Constructions
  • The Perfect Split — Constructing the perpendicular bisector · Constructions
  • The Perpendicular Drop — constructing right angles from outside · Constructions
  • The SSS Triangle Builder — Three sides, one perfect triangle · Constructions
  • SAS Triangle Builder — Two sides and the included angle · Constructions
  • The ASA Triangle Builder — Two angles and a side lock the shape in place · Constructions
  • The Solid Box — Length, breadth, and height come together · Recognition of Solids
  • The Cuboid's Structure — six faces, twelve edges, eight vertices · Recognition of Solids
  • The Cube's Blueprint — six equal squares, twelve equal edges · Recognition of Solids
  • Meet the Cylinder — Two flat faces, one curved side · Recognition of Solids
  • The Sphere's Secret — every surface point keeps the same distance · Recognition of Solids
  • Meet the Cone — Tapering from a circle to a point · Recognition of Solids
  • Meet the Prism — Two congruent bases, parallel sides · Recognition of Solids
  • The Pyramid's Peak — base, faces, and a common vertex · Recognition of Solids
  • From Flat to 3D — Discover how nets build solids · Recognition of Solids
  • The Oblique Sketch — True shapes, slanted sides, recognizable solids · Recognition of Solids
  • What is a Region? — Interior + Boundary = Region · Perimeter and Area of Plane Figures
  • The Boundary Walk — Perimeter is the distance around a shape · Perimeter and Area of Plane Figures
  • Rectangle's Perimeter Race — 2 times (length + breadth) · Perimeter and Area of Plane Figures
  • Perimeter of a Square — Four equal sides, one simple rule · Perimeter and Area of Plane Figures
  • The Triple Side — Perimeter of an equilateral triangle · Perimeter and Area of Plane Figures
  • The Area Concept — boundary plus interior · Perimeter and Area of Plane Figures
  • Area of a Rectangle — length times breadth · Perimeter and Area of Plane Figures
  • The Square's Secret — Why area is always side squared · Perimeter and Area of Plane Figures

Class 7

  • The Area of a Product — Visualizing monomial multiplication · Fundamental Concepts
  • Area of the Whole — Visualizing polynomial multiplication · Fundamental Concepts
  • The Area Model of Division — Visualizing polynomial division with rectangles · Fundamental Concepts
  • The Birth of an Angle — two rays, one vertex, infinite possibilities · Lines and Angles
  • The Geometry Basics — Point, Line, Ray, and Segment defined · Lines and Angles
  • Angle Classifiers — Acute, Right, Obtuse, Straight & Reflex · Lines and Angles
  • The Crossing Lines — vertically opposite angles are always equal · Lines and Angles
  • The 90° and 180° Pairs — Complementary and supplementary angles · Lines and Angles
  • The Transversal Bridge — crossing lines, creating angle pairs · Lines and Angles
  • Parallel Lines & Transversals — alternate, corresponding & co-interior angles · Lines and Angles
  • The Parallel Promise — equal alternate angles mean parallel lines · Lines and Angles
  • The Three-Sided Promise — Always closed, always three sides · Triangles
  • The Exterior Angle Theorem — The outside angle equals the two inside opposites · Triangles
  • The 180° Rule — Every triangle's angles add up to a straight line · Triangles
  • The Angle Identity — Acute, Right, or Obtuse — what's your triangle's name? · Triangles
  • Triangle Types by Sides — Scalene, Isosceles, Equilateral · Triangles
  • The Equilateral Promise — every corner locked at 60° · Triangles
  • The Isosceles Balance — Equal sides guarantee equal base angles · Triangles
  • The Longest Side — Discovering the hypotenuse in right triangles · Pythagoras Theorem
  • The Pythagorean Promise — hypotenuse squared equals the sum of the legs squared · Pythagoras Theorem
  • The Converse Connection — When sides match, the angle snaps to 90° · Pythagoras Theorem
  • The Side-Length Secret — How squares reveal the triangle's true nature · Pythagoras Theorem
  • The Fold Test — Finding the line that makes both halves match · Symmetry
  • Folding the Square — Discovering 4 lines of symmetry · Symmetry
  • The Mirror's Promise — Reflection and the perpendicular bisector · Symmetry
  • Mirror on the X-Axis — flipping coordinates with symmetry · Symmetry
  • Mirror on the Y-Axis — watch x flip sign while y stays put · Symmetry
  • Reflection in Origin — flip both signs, stay opposite · Symmetry
  • Spin & Stay the Same — Rotation preserves shape and size · Symmetry
  • Spin & Match — Discovering rotational symmetry and order · Symmetry
  • The Square's Spin — rotational symmetry of order 4 · Symmetry
  • Rotational Symmetry of an Equilateral Triangle — Fits onto itself 3 times in a full turn · Symmetry
  • The 3D Promise — Length, Breadth, Height — the solid's signature · Recognition of Solids
  • The Cube's Perfect Symmetry — Six equal faces, twelve equal edges · Recognition of Solids
  • The Cuboid Code — 6 faces, 12 edges, 8 vertices — always · Recognition of Solids
  • The Cone's Blueprint — vertex, edge, and two surfaces · Recognition of Solids
  • The Cylinder's Blueprint — 3 faces, 2 edges, 0 vertices—always · Recognition of Solids
  • The Magic of Polyhedra — V + F – E = 2 always holds · Recognition of Solids
  • The Cube's Net — folding flat patterns into 3D solids · Recognition of Solids
  • Map Scale Magic — Turning map measurements into real-world distances · Recognition of Solids
  • Coincide & Congruent — Same shape, same size, perfect match · Congruency: Congruent Triangles
  • The Coincidence Test — When two triangles land perfectly on top of each other · Congruency: Congruent Triangles
  • The Mirror Match — When triangles are congruent, every part lines up perfectly · Congruency: Congruent Triangles
  • SSS Congruence Criterion — Three equal sides guarantee congruence · Congruency: Congruent Triangles
  • SAS Congruence Criterion — Two sides and the included angle lock the shape · Congruency: Congruent Triangles
  • ASA Congruence Criterion — Two angles and the included side lock the triangle · Congruency: Congruent Triangles
  • AAS Congruence Criterion — Two angles and a side lock the triangle · Congruency: Congruent Triangles
  • RHS Congruence Criterion — Right angle, Hypotenuse, Side · Congruency: Congruent Triangles
  • AAA: The Size Trap — Same angles, different sizes · Congruency: Congruent Triangles
  • Parallel Sides → Congruent Triangles — AB ∥ CD and AB = CD ⇒ △AOB ≅ △DOC by ASA · Congruency: Congruent Triangles
  • The Isosceles Mirror — RHS congruence in action · Congruency: Congruent Triangles
  • Copy That Angle! — Construct a congruent angle using arcs and radii · Constructions
  • Splitting the Angle — The art of making two equal halves · Constructions
  • The 60° Lock — How matching arcs lock into a perfect angle · Constructions
  • The Perfect Right Angle — Constructing 90° with compass and straightedge · Constructions
  • The Perfect Split — Bisecting a line segment with precision · Constructions
  • The Perpendicular Promise — always at right angles to the line · Constructions
  • The Perpendicular Drop — Constructing a right angle from outside · Constructions
  • The Parallel Path — equal angles, forever parallel · Constructions
  • The SSS Blueprint — Building triangles from three sides · Constructions
  • The Isosceles Blueprint — Base and angles, meet at the peak · Constructions
  • The Equilateral Blueprint — three sides, three equal arcs · Constructions
  • The Right Triangle Blueprint — building with two legs and a perfect corner · Constructions
  • The Hypotenuse Rule — Constructing right triangles from side & hypotenuse · Constructions
  • The Circle That Holds It All — Constructing the circumcircle of a triangle · Constructions
  • The Triangle's Inner Circle — hugging all three sides perfectly · Constructions
  • Boundaries and Spaces — Understanding Perimeter and Area · Mensuration
  • The Area Multiplier — How length units become area units · Mensuration
  • The Rectangle's Boundary — always twice the sum of length and breadth · Mensuration
  • The Square's Secret Count — perimeter is always 4 times the side · Mensuration
  • Triangle's Total Length — Adding up the three sides · Mensuration
  • The Circle's Edge — always 2π times the radius · Mensuration
  • Area of a Circle — π r²: The magic formula · Mensuration
  • Heron's Secret Formula — Find any triangle's area from just its three sides · Mensuration
  • The Rectangle's Area — length times breadth, every time · Mensuration
  • Square's Secret Area — Side squared or diagonal squared divided by 2 · Mensuration
  • The Triangle's Secret — half base times height, every time · Mensuration
  • Base Meets Height — Why area is always base times height · Mensuration
  • The Rhombus Area Secret — half the product of diagonals · Mensuration

Class 8

  • Curves & Regions — Open, closed, and simple closed curves · UNDERSTANDING SHAPES (Including Polygons)
  • The Polygon Puzzle — Closed, straight, and no crossing lines · UNDERSTANDING SHAPES (Including Polygons)
  • The Polygon's Angle Secret — how diagonals unlock the sum of interior angles · UNDERSTANDING SHAPES (Including Polygons)
  • The 360° Rule — Exterior angles always sum to a full circle · UNDERSTANDING SHAPES (Including Polygons)
  • The Regular Polygon's Secret — Angles, sides, and the magic of n · UNDERSTANDING SHAPES (Including Polygons)
  • The Parallelogram's Balance — Opposite sides & angles always match · Special Types of Quadrilaterals
  • The Diagonal Promise — always cut each other in half · Special Types of Quadrilaterals
  • The Rectangle's Diagonals — equal length, mutual bisectors · Special Types of Quadrilaterals
  • The Rhombus Cross — diagonals that always bisect at right angles · Special Types of Quadrilaterals
  • Diagonals of a Square — equal, bisecting, and perpendicular · Special Types of Quadrilaterals
  • The Isosceles Trap — Equal sides, equal diagonals, parallel bases · Special Types of Quadrilaterals
  • The Kite's Balance — adjacent sides equal, diagonals perpendicular · Special Types of Quadrilaterals
  • Building Angles from Scratch — Construct 60°, 90°, 45°, and 30° with ruler and compass · CONSTRUCTIONS (Using ruler and compasses only)
  • The Angle Splitter — Dividing angles into equal halves · CONSTRUCTIONS (Using ruler and compasses only)
  • The Perfect Split — Cutting a segment exactly in half at a right angle · CONSTRUCTIONS (Using ruler and compasses only)
  • The Parallel Promise — equal alternate angles, forever parallel · CONSTRUCTIONS (Using ruler and compasses only)
  • The Square's Blueprint — equal sides, right angles, perfect symmetry · CONSTRUCTIONS (Using ruler and compasses only)
  • The Polyhedron's Faces — Bounded by polygons, not curves · Representing 3-d in 2-d
  • Faces, Edges, and Vertices — Counting the parts of a polyhedron · Representing 3-d in 2-d
  • Unfolding Solids — From 3D shapes to flat patterns · Representing 3-d in 2-d
  • The Mirror Line — folding figures into perfect halves · Symmetry (including Reflection and Rotation)
  • The Circle's Infinite Mirror — every diameter splits it perfectly in half · Symmetry (including Reflection and Rotation)
  • Lines of Symmetry in Regular Polygons — n sides always mean n lines of perfect balance · Symmetry (including Reflection and Rotation)
  • Mirror Image at Zero — Reflection of a point in the origin · Symmetry (including Reflection and Rotation)
  • Mirror Image on the Axis — how reflection flips the y-coordinate · Symmetry (including Reflection and Rotation)
  • Reflection in the Y-Axis — Mirrors across the y-axis · Symmetry (including Reflection and Rotation)
  • The 180° Flip — rotating points through the origin · Symmetry (including Reflection and Rotation)
  • The 90° Spin — swapping coordinates with a sign flip · Symmetry (including Reflection and Rotation)
  • Heron's Secret Code — Area from sides alone, every time · Area of a Trapezium and a Polygon
  • The Triangle's Secret — Area depends only on base and height · Area of a Trapezium and a Polygon
  • The Rectangle's Rhythm — how length and breadth dictate area and perimeter · Area of a Trapezium and a Polygon
  • Square Secrets — Perimeter, Area, and Diagonal formulas · Area of a Trapezium and a Polygon
  • The Trapezium's Secret — Area = ½ × (a + b) × h · Area of a Trapezium and a Polygon
  • The Parallelogram's Secret — base times height, every time · Area of a Trapezium and a Polygon
  • The Rhombus Area Secret — Diagonals hold the key to the area · Area of a Trapezium and a Polygon
  • The Circle's Area — how radius unlocks the formula · Area of a Trapezium and a Polygon
  • The Circle's Perimeter — Unwrapping the circumference formula · Area of a Trapezium and a Polygon
  • Volume, Capacity & Surface Area — The three pillars of 3D measurement · SURFACE AREA, VOLUME AND CAPACITY (Cuboid, Cube and Cylinder)
  • Cuboid Dimensions — Volume, Surface Area, and Diagonal · SURFACE AREA, VOLUME AND CAPACITY (Cuboid, Cube and Cylinder)
  • The Cube's Secrets — Volume, Surface Area, and Diagonals · SURFACE AREA, VOLUME AND CAPACITY (Cuboid, Cube and Cylinder)
  • The Box's Hidden Core — external vs internal dimensions · SURFACE AREA, VOLUME AND CAPACITY (Cuboid, Cube and Cylinder)
  • Cylinder Formulas Unrolled — CSA, TSA, and Volume from first principles · SURFACE AREA, VOLUME AND CAPACITY (Cuboid, Cube and Cylinder)

Class 9

  • The Equal Sides Rule — equal sides lock equal angles · Triangles [Congruency in Triangles]
  • Sides & Angles: The Great Match — bigger side always faces bigger angle · Triangles [Congruency in Triangles]
  • The Triangle's Secret Sum — Angles always add up to 180° · Triangles [Congruency in Triangles]
  • Same Shape, Same Size — The definition of congruent triangles · Triangles [Congruency in Triangles]
  • CPCTC: The Mirror Rule — Congruent triangles keep matching parts equal · Triangles [Congruency in Triangles]
  • AAS Congruence Criterion — Two Angles, One Side · Triangles [Congruency in Triangles]
  • The ASA Match — Two angles and the included side lock the triangle · Triangles [Congruency in Triangles]
  • The RHS Rule — Hypotenuse & side guarantee congruence · Triangles [Congruency in Triangles]
  • SAS: The Rigid Triangle — Two sides and the included angle lock the shape · Triangles [Congruency in Triangles]
  • Three Sides, One Shape — SSS Congruency Theorem · Triangles [Congruency in Triangles]
  • Two Sides, One Rule — Discovering isosceles & equilateral triangles · Isosceles Triangles
  • Isosceles Triangle Theorem — equal sides always hide equal angles · Isosceles Triangles
  • Isosceles Triangle Converse — The secret symmetry of isosceles triangles · Isosceles Triangles
  • Angle Chase: Parallel Lines & a Hidden Isosceles Triangle — Find a, b and c using alternate angles, the exterior angle, and equal base angles · Isosceles Triangles
  • Angle Chase: Nested Isosceles Triangles — nested isosceles triangles always hide a 3:1 ratio · Isosceles Triangles
  • The Bisector's Balance — Why AO always splits the vertex angle · Isosceles Triangles
  • The Triangle's Unbreakable Rule — why two sides always beat the third · Inequalities
  • The Difference Rule — Two sides can't differ by more than the third · Inequalities
  • The Greater Side's Secret — Why longer sides face bigger angles · Inequalities
  • The Greater Angle's Side — If angles differ, opposite sides follow suit · Inequalities
  • The Perpendicular Promise — Why the shortest path is always straight down · Inequalities
  • The Median's Secret — Why two sides always beat twice the median · Inequalities
  • The Midpoint Bridge — parallel, proportional, and perfectly half · Mid-point Theorem and Its Converse [Including Intercept Theorem]
  • The Midpoint Mirror — parallel lines always bisect the third side · Mid-point Theorem and Its Converse [Including Intercept Theorem]
  • The Equal Intercept Theorem — Parallel lines cut transversals in matching ratios · Mid-point Theorem and Its Converse [Including Intercept Theorem]
  • The Trapezium Midsegment — half the sum of the parallel sides · Mid-point Theorem and Its Converse [Including Intercept Theorem]
  • The Pythagorean Balance — squares on legs equal square on hypotenuse · Pythagoras Theorem [Proof and Simple Applications with Converse]
  • The Similarity Shortcut — Pythagoras proved through matching triangles · Pythagoras Theorem [Proof and Simple Applications with Converse]
  • The Converse Check — When squares match, the angle is right · Pythagoras Theorem [Proof and Simple Applications with Converse]
  • Triangle Classification by Sides — How side lengths dictate angle types · Pythagoras Theorem [Proof and Simple Applications with Converse]
  • The Parallelogram Law — diagonals squared sum equals sides squared sum · Pythagoras Theorem [Proof and Simple Applications with Converse]
  • Opposite Sides Equal — The parallelogram's hidden symmetry · Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
  • The Parallelogram's Mirror — Opposite angles are always equal · Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
  • The Parallelogram Key — One pair equal & parallel unlocks the shape · Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
  • The Angle Sum Secret — Why every n-gon hides (2n-4) right angles · Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
  • The Regular Polygon's Secret — Equal sides, equal angles, perfect symmetry · Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
  • The Four-Sided Promise — Angles always add up to 360° · Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
  • Parallel Pairs & Slides — parallelogram vs trapezium definitions · Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
  • The Quadrilateral Chameleon — Morphing between Rectangle, Rhombus, and Square · Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
  • The Diagonals' Balance — always bisect each other · Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
  • The Rhombus Cross — diagonals always meet at 90° · Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
  • The Rectangle's Balance — Why diagonals always match in length · Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
  • Square's Diagonals — equal lengths, perfect right angles · Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
  • The Four-Sided Puzzle — Construct any quadrilateral from 4 sides & 1 angle · Construction of Polygons [Using Ruler and Compass Only]
  • Locking the Quadrilateral — 3 sides, 2 angles, one unique shape · Construction of Polygons [Using Ruler and Compass Only]
  • The Parallelogram Blueprint — Two sides and an angle are all you need · Construction of Polygons [Using Ruler and Compass Only]
  • The Bisecting Diagonals — Construct a parallelogram from side and diagonals · Construction of Polygons [Using Ruler and Compass Only]
  • The Hexagon's Secret — Side length equals radius every time · Construction of Polygons [Using Ruler and Compass Only]
  • Between the Same Parallels — Same height, different shapes · Area Theorems [Proof and Use]
  • Same Height, Different Base — Area ratio follows the base ratio · Area Theorems [Proof and Use]
  • Same Base, Same Parallels — Why two parallelograms always share the same area · Area Theorems [Proof and Use]
  • Same Base, Same Parallels — Why a triangle is always half its parallelogram twin · Area Theorems [Proof and Use]
  • Same Base, Same Height — why parallel lines lock in equal areas · Area Theorems [Proof and Use]
  • The Median's Equal Share — splitting any triangle's area perfectly in two · Area Theorems [Proof and Use]
  • The Circle's Promise — A point's journey at a constant distance from a fixed centre · Circle
  • Arcs, Segments & Sectors — The three key regions of a circle · Circle
  • The Bisector's Promise — perpendicular to every chord it meets · Circle
  • The Unique Circle — Three points, one circle, no more, no less · Circle
  • Equal Arcs, Equal Angles — The central angle dictates the arc length · Circle
  • Perimeter vs. Area — Boundary length vs. surface measure · Area and Perimeter of Plane Figures
  • Heron's Formula Unveiled — Area from sides alone · Area and Perimeter of Plane Figures
  • Area of a Triangle Formula — Base, height, and the magic of 1/2 · Area and Perimeter of Plane Figures
  • Area of an Equilateral Triangle — √3/4 a², every time · Area and Perimeter of Plane Figures
  • Half the Rectangle — Area of a right-angled triangle · Area and Perimeter of Plane Figures
  • The Diagonal Split — Area of a quadrilateral in one formula · Area and Perimeter of Plane Figures
  • Area Unlocked — base × height and diagonals × half · Area and Perimeter of Plane Figures
  • Area & Perimeter: Rect & Square — Master the formulas by dragging and exploring · Area and Perimeter of Plane Figures
  • The Trapezium's Secret — area hides in the parallel sides and height · Area and Perimeter of Plane Figures
  • The Circle's Boundary — Unwrapping the mystery of 2πr · Area and Perimeter of Plane Figures
  • The Circle's Area — πr² revealed through play · Area and Perimeter of Plane Figures
  • The Solid's Shape — Volume, Surface Area, and Space · Solids
  • The Cuboid's Diagonal — Uncovering the space diagonal with Pythagoras · Solids
  • The Cube's Diagonal — always √3 times the edge · Solids
  • The Slice That Never Changes — Uniform cross-sections and volume shortcuts · Solids
  • Flow of Water Through a Pipe — Volume = Area × Speed · Solids
  • The Variable Boss — Who leads and who follows in a linear equation? · Co-ordinate Geometry
  • The Order Matters — Why (3, -2) is not the same as (-2, 3) · Co-ordinate Geometry
  • Meet the Cartesian Plane — Two axes, one origin, infinite possibilities · Co-ordinate Geometry
  • Coordinates of Points — Mastering the Cartesian Plane · Co-ordinate Geometry
  • The Four Quadrants — mapping signs to the coordinate plane · Co-ordinate Geometry
  • Plotting Points — Navigate the coordinate plane · Co-ordinate Geometry
  • The Constant Lines — x=0, y=0, x=a, y=a on the coordinate plane · Co-ordinate Geometry
  • Plotting the Line — Connecting points to reveal the graph · Co-ordinate Geometry
  • Angle of the Line — How steep is your line? · Co-ordinate Geometry
  • Slope & Inclination — m = tan θ · Co-ordinate Geometry
  • The Y-Intercept — Where the line crosses the vertical axis · Co-ordinate Geometry
  • Slope & Y-Intercept Unlocked — Decode y = mx + c visually · Co-ordinate Geometry
  • Distance Formula Unveiled — See why √(Δx)² + (Δy)² always works · Distance Formula
  • Distance from the Origin — always √x² + y² · Distance Formula
  • The Circumcentre's Secret — Always equidistant from the vertices · Distance Formula
  • The Collinear Condition — when distances add up perfectly · Distance Formula

Class 10

  • Coordinates & Axes — Finding your place on the plane · Reflection (In x-axis, y-axis, x = a, y = a and the origin; Invariant Points)
  • The Mirror's Rule — Reflection as a perpendicular bisector · Reflection (In x-axis, y-axis, x = a, y = a and the origin; Invariant Points)
  • Mirror Image on the Axis — Reflection in the x-axis: (x, y) → (x, -y) · Reflection (In x-axis, y-axis, x = a, y = a and the origin; Invariant Points)
  • Mirror, Mirror on the Y-Axis — Watch how coordinates flip when you cross the line x = 0 · Reflection (In x-axis, y-axis, x = a, y = a and the origin; Invariant Points)
  • Reflection in Origin — Flip across the center, signs both change · Reflection (In x-axis, y-axis, x = a, y = a and the origin; Invariant Points)
  • The Unmoved Point — discovering invariant points under reflection · Reflection (In x-axis, y-axis, x = a, y = a and the origin; Invariant Points)
  • Mirror Across x = a — how parallel lines dictate reflection coordinates · Reflection (In x-axis, y-axis, x = a, y = a and the origin; Invariant Points)
  • The Section Formula — Dividing segments with precision · Section Formula and Mid-Point Formula
  • The Trisection Trick — splitting segments into three equal parts · Section Formula and Mid-Point Formula
  • The Mid-Point Promise — always exactly halfway between · Section Formula and Mid-Point Formula
  • The Balance Point — Where the medians meet · Section Formula and Mid-Point Formula
  • Rise Over Run — The secret formula for a line's steepness · Equation of a Line
  • Slopes of Parallel Lines — equal slopes, forever parallel · Equation of a Line
  • The Slope Product Rule — why perpendicular lines multiply to –1 · Equation of a Line
  • The Collinearity Check — When three points share a single line · Equation of a Line
  • The Slope-Intercept Form — y = mx + c: where steepness meets the y-axis · Equation of a Line
  • The Point-Slope Promise — how a fixed point and a slope define a line · Equation of a Line
  • Two Points, One Line — Deriving the equation from any two coordinates · Equation of a Line
  • Same Shape, Different Size — Exploring the definition of similar figures · Similarity (With Applications to Maps and Models)
  • The Shape-Shifting Rule — Equal angles, proportional sides · Similarity (With Applications to Maps and Models)
  • Matching Sides & Angles — How similarity pairs up triangle parts · Similarity (With Applications to Maps and Models)
  • The Angle-Angle Match — When two angles align, triangles scale perfectly · Similarity (With Applications to Maps and Models)
  • The SAS Similarity Rule — Equal angle, proportional sides · Similarity (With Applications to Maps and Models)
  • The SSS Similarity Rule — Proportional sides mean identical shapes · Similarity (With Applications to Maps and Models)
  • The Parallel Divider — BPT: Parallel lines cut sides proportionally · Similarity (With Applications to Maps and Models)
  • Area Ratio of Similar Triangles — Areas scale with the square of the sides · Similarity (With Applications to Maps and Models)
  • The Moving Trail — Discovering the path of a point · Loci (Locus and Its Constructions)
  • The Bisector's Balance — equidistant from intersecting lines · Loci (Locus and Its Constructions)
  • The Equidistant Locus — always the perpendicular bisector · Loci (Locus and Its Constructions)
  • The Locus Explorer — Where do points go when they follow the rules? · Loci (Locus and Its Constructions)
  • The Four Triangle Hearts — Where medians, bisectors, and altitudes meet · Loci (Locus and Its Constructions)
  • The Centre's Double — angle at centre is twice angle at circumference · Circles
  • Angles in the Same Segment — equal angles, same chord, same arc · Circles
  • The Semi-Circle Secret — why angles on a diameter always hit 90° · Circles
  • The Cyclic Balance — opposite angles always sum to 180° · Circles
  • The Exterior Angle Secret — cyclic quads hide a beautiful equality · Circles
  • The Chord's Mirror — how the centre always bisects at right angles · Circles
  • Equal Chords, Equal Distances — why symmetry keeps chords balanced from the centre · Circles
  • Equal Chords, Equal Angles — why matching chords always match their centre angles · Circles
  • Tangent, Secant, & Point of Contact — One touch vs. two cuts · Tangents and Intersecting Chords
  • The Twin Tangents — equal lengths, equal angles, one line of symmetry · Tangents and Intersecting Chords
  • The Tangent's Promise — always at right angles to the radius · Tangents and Intersecting Chords
  • The Line of Centres — where touching circles meet · Tangents and Intersecting Chords
  • The Chord Intersection Secret — PA × PB always equals PC × PD · Tangents and Intersecting Chords
  • The Alternate Segment Secret — tangent-chord angle always equals alternate angle · Tangents and Intersecting Chords
  • The Tangent-Secant Secret — PA × PB always equals PT² · Tangents and Intersecting Chords
  • The Tangent's Promise — always at right angles to the radius · Constructions (Circles)
  • Tangents from the Outside — equal lengths, perfect right angles · Constructions (Circles)
  • The Circumcircle Quest — Finding the center that binds all vertices · Constructions (Circles)
  • The Incenter's Promise — equidistant from every side · Constructions (Circles)
  • The Hexagon's Circle — circumscribing a regular hexagon · Constructions (Circles)
  • The Hexagon's Inner Circle — finding the perfect inscribed circle · Constructions (Circles)
  • The Cylinder's Anatomy — Surface, space, and slices · Cylinder, Cone and Sphere (Surface Area and Volume)
  • The Hollow Cylinder's Secret — Volume and surface area formulas · Cylinder, Cone and Sphere (Surface Area and Volume)
  • The Cone's Blueprint — h, r, and l in perfect harmony · Cylinder, Cone and Sphere (Surface Area and Volume)
  • Sphere Formulas — Volume and Surface Area · Cylinder, Cone and Sphere (Surface Area and Volume)
  • Half a Sphere's Secrets — Volume and surface area of a hemisphere · Cylinder, Cone and Sphere (Surface Area and Volume)
  • The Toy Maker's Formula — Adding up curved areas and volumes · Cylinder, Cone and Sphere (Surface Area and Volume)
  • Up and Down Angles — elevation meets depression · Heights and Distances
  • The Sun's Shadow Angle — how height and shadow reveal the sun's elevation · Heights and Distances
  • The Tower's Height — using tangent to measure the sky · Heights and Distances
  • Angle of Depression — From tower top to sea level · Heights and Distances
  • The Stretching Shadow — how sun angles reveal hidden heights · Heights and Distances
  • The Car's Countdown — From 30° to the tower's base · Heights and Distances
  • Chasing the Cloud's Height — using angles of elevation and depression · Heights and Distances
  • Climbing the Tangent — finding tower height from walking distances · Heights and Distances
  • Pole & Tower Heights — Unlocking distances with angles of elevation · Heights and Distances
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