Unit 4: Shapes

Look around you — every short-eat on the table has a shape! Gulha is round, bajiyaa is triangular, bis keemiyaa is rectangular, havaadhlee bis is oval. In this unit you will name shapes, list their properties, and discover the hidden symmetry in polygons.

Look around and list every shape you can see. Split them into 2D (flat) and 3D (solid). A polygon is a flat (2D) closed shape with straight sides — no curves allowed.

A regular polygon has all sides equal AND all angles equal. An irregular polygon has sides of different lengths or angles of different sizes. An equilateral triangle is regular; a scalene triangle is irregular. A square is regular; a rhombus is not (equal sides but unequal angles).

A regular pentagon has 5 equal sides and 5 equal angles of 108°. A rhombus has 4 equal sides but its angles are not all equal (e.g. 138° and 42°), so it is irregular. Equal sides alone are NOT enough — angles must match too.

Triangles can be sorted by sides or by angles.

Among triangles, only the equilateral triangle is regular (all 3 sides AND all 3 angles equal — each 60°). Isosceles, scalene, acute, obtuse and right triangles are all irregular.

All quadrilaterals have 4 sides — but each special quadrilateral has its own rule:

Not every closed shape is a polygon. A polygon must be flat, closed, and made of straight sides only. A circle has a curved side, so it's NOT a polygon. Shapes with gaps are not polygons either.

To classify a polygon: check if all sides are equal AND all angles are equal. If even one differs, it's irregular. A tilted square is still regular — orientation doesn't matter, only sides and angles.

On grid paper, try drawing two regular polygons (like a square and an equilateral triangle) and two irregular polygons (like a scalene triangle and a kite). Naming them helps you remember their properties.

Use a ruler to measure all 3 sides of a triangle. Then sort:

Use a protractor to read all 3 angles. Then sort:

To draw a triangle given two angles and one side (e.g. 11 cm side with 60° and 44° at its ends), use a ruler and protractor. Once drawn, you can check: with no equal sides and no right angle, it's a scalene acute triangle.

Looking at a shape, ask: How many right angles? Are opposite sides equal? Are all sides equal? A shape with 4 equal sides and 4 right angles is a square. A shape with one pair of parallel sides only is a trapezium. A diamond with 4 equal sides but no right angles is a rhombus.

Mark the right angles (90°) with a small square in the corner. Mark parallel sides with matching arrows.

A quadrilateral is a polygon with 4 straight sides and 4 angles. An example is a rectangle. A non-example is a triangle (only 3 sides). Discuss similarities and differences between rhombus, parallelogram and trapezium with a friend.

Stand in front of a mirror — you see yourself the same distance behind the glass as you are in front of it. A figure is symmetrical if it can be divided into two equal parts so that each part is a mirror image of the other. Butterflies, flowers and a swan's reflection in water are all symmetrical.

Given half of a symmetric figure and its line of symmetry (the dashed line), you can complete the figure by drawing the exact mirror image on the other side. Every point on the original must have a matching point the same distance from the line.

Some shapes have line symmetry (star, equilateral triangle, regular pentagon, semicircle), some don't (curly arrow, crescent moon, lowercase 'e'). Try folding: if both halves match exactly, the fold is a line of symmetry. If not, the shape has no line of symmetry there.

For regular polygons, the number of lines of symmetry equals the number of sides.

Irregular shapes have fewer (or zero) lines.

Some shapes look the same after being turned around their centre. A flower with 4 petals fits onto itself at ¼ turn, ½ turn, ¾ turn and a full turn — 4 matches per complete spin. We say it has rotational symmetry of order 4.

Spin a rhombus about its centre. After 90° it does NOT match. After 180° it matches (Order 1). After 270° it doesn't. After a full 360° turn it matches again (Order 2). So a rhombus has rotational symmetry of order 2.

A shape has rotational symmetry if it matches itself at least once before a full turn. A regular hexagon and a sun-shape (many points) do. A plain arrow and a crescent moon do NOT — they only match after a full 360° turn (order 1, which we usually say means 'no rotational symmetry').

Examples of order:

For regular polygons, the order equals the number of sides.

Common shape orders:

Shapes, angles, measurement and symmetry are used by builders, designers, architects, engineers and jewellers every day. Mosques, the Taj Mahal, modern skyscrapers and decorative ceilings all start as sketches with careful symmetry.

True or false: 'All triangles have three lines of symmetry.' Only equilateral triangles do (3 lines). Isosceles triangles have just 1, and scalene triangles have 0. So the statement is false.

A rectangle has 4 right angles — but a square is the only quadrilateral with 4 right angles AND 4 equal sides.

Hakeem says: 'All isosceles triangles are equilateral.' Faisal says: 'All equilateral triangles are isosceles.' Faisal is right! Equilateral means 3 equal sides, which is more than the 2-equal-sides isosceles rule needs — so every equilateral fits the isosceles definition, but not the other way around.

Huzaima asked: 'Is a rectangle the ONLY quadrilateral with rotational symmetry of order 2?' No — a rhombus and a parallelogram also have order 2. The pattern for regular polygons: order of rotational symmetry = number of sides.

For each regular polygon, count sides and lines of symmetry:

Shiha makes a pattern using isosceles triangles — each has 1 line of symmetry. A window with 4 right angles, 2 pairs of parallel sides, but sides of different lengths is a rectangle.

To reflect a polygon in a mirror line: take each corner and measure its distance from the line. Plot the matching point the SAME distance on the other side. Join the new points to get the reflected shape — same size, flipped direction.

Reflections work with vertical and horizontal mirror lines. A triangle above a horizontal mirror line appears below it, flipped upside down. A trapezium to the left of a vertical mirror appears to the right, flipped left-right.

Big ideas of this unit: