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Geometry and Measures

Geometry and Measures

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Shapes and Angles

Illustrating polygons as 2D closed shapes with straight line segments, showing a triangle and star, and non-polygons like curved shape and 3D cube.
Grade 7

Polygons and Types of Quadrilaterals

A polygon is a 2D closed shape with straight edges. Learn the properties of quadrilaterals like…
Illustration of acute, right, obtuse, straight, reflex, and full angles, with corresponding angle measures.
Grade 7

Measurement and Types of Angles

An angle is formed when two rays meet at a vertex. Explore acute, right, obtuse, straight, reflex, a…
Definition, notation, and visualisation of line segments, rays, and lines.
Grade 7

Perpendicular and Parallel Lines

Perpendicular lines intersect at 90°, while parallel lines stay equidistant and never intersect…
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Triangles and Constructions

A triangle with vertices A, B, and C, sides a, b, and c, and angles ?, ?, and ?. The vertices are labelled counterclockwise.
Grade 9

Constructing Triangles

Learn how to construct triangles using ASA, SSS, and SSA methods with a compass, ruler & protractor…
Congruent triangles criteria with examples showing two triangles with same side lengths and angle sizes.
Grade 9

Congruent Triangles

Congruent triangles are identical in size and shape, with equal side lengths and angles. Learn the…
Explanation of Thales' Theorem with a diagram showing a right-angled triangle formed by a diameter and any point on a semicircle.
Grade 10

Thales' Theorem

Thales’ Theorem states that any triangle formed with a circle’s diameter as one side is always a…
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Volume and Surface Area

Showing the properties of solids, focusing on cuboids and cubes, with details on vertices, edges, and faces, comparing rectangle and square faces.
Grade 7

Solids and Units of Volume

Solids are 3D shapes with length, width, and height, like cuboids. Learn common units of volume (mm³…
Diagram showing the volume formulas of a cuboid and a cube. Cuboid: 5 cm x 3 cm x 2 cm, volume 30 cm³. Cube: 5 cm sides, volume 125 cm³.
Grade 7

Volume of a Cuboid and Cube

The volume of a cuboid is calculated as V = length × width × height, and the volume of a cube is V…
Illustration showing surface area formulas for a cuboid and a cube. The cuboid formula is 2lw + 2lh + 2hw, and the cube formula is 6a².
Grade 7

Surface Area of Solids

The surface area of a solid is the total area of all its faces. Learn surface area formulas for cube…
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Area and Perimeter

Diagram explaining the area of triangles formula 1/2 × b × h, examples of perpendicular height, and notes emphasising any side as base.
Grade 7

Area of a Triangle

Learn how to find the area of a triangle using the formula ½ × base × height. Explore step-by-step…
Diagram showing the formula for the area of a parallelogram, A = b?h, with labelled base (b) and height (h) on two parallelograms.
Grade 10

Area of Parallelograms and Triangles

How to find the height and area of parallelograms and triangles using base and height formulas…
Perimeter of a rectangle and square with formulas. Rectangle: length 5 cm, width 3 cm, perimeter 16 cm. Square: side 2 m, perimeter 8 m.
Grade 7

Perimeter of a Polygon

To find the perimeter of a polygon, add the lengths of all sides. Learn perimeter formulas for…
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Transformation and Symmetry

Diagram showing lines of symmetry in common shapes: rectangle (2), square (4), isosceles triangle (1), equilateral triangle (3), circle (infinite).
Grade 7

Line of Symmetry and Reflection Symmetry

A line of symmetry divides a shape into two identical halves. Learn to find how many lines of…
Diagram showing a square with an order of rotation symmetry 4, and explanations of the centre of rotation, angle of rotation, and order of symmetry.
Grade 7

Rotational Symmetry

A shape has rotational symmetry if it looks the same when rotated less than 360°. Learn the center,…
Column vectors with visual examples. Describes horizontal and vertical shifts using positive and negative values.
Grade 8

Translating Shapes

Translating shapes means moving them on a grid without changing size or orientation. Learn how to…
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Trigonometry

Diagram explaining Pythagoras theorem using two right-angled triangles, showing the equation a² + b² = c², and an example showing 3² + 4² = 5².
Grade 11

Pythagoras Theorem

In a right-angled triangle, a² + b² = c². Learn how to use it to find missing sides and calculate…
Definitions, ratios, and visuals of sine, cosine, and tangent shown in a right triangle.
Grade 12

Trigonometry: Sine, Cosine, Tangent

Basic trigonometry ratios – how to use sin, cos, and tan to find missing sides or angles in right…
Cosine Rule formula a² = b² +c² -2bc·cos(A) explained with a triangle diagram labelled with sides a, b, c, and angle A.
Grade 12

Cosine Rule

Apply the Cosine Rule to find sides and angles in non-right triangles using trigonometric methods….
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Shapes and Angles
Triangles and Constructions
Volume and Surface Area
Area and Perimeter
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