Understanding Quadrilaterals
Class 8 · Mathematics
5 ideas in Class 8 Mathematics, explained in plain words, with games and quizzes to practise.
Convex, Concave and Regular Polygons
Part of: Polygons and angles
A polygon is a closed shape made of straight line segments. A convex polygon has no dents, so every diagonal lies inside it. A concave polygon has a dent, so some diagonal goes outside. A regular polygon has all sides equal and all angles equal, like a square or an equilateral triangle.
Why it matters. Sorting shapes by their properties is the base of geometry. Children who think 'equal sides' alone makes a shape regular will mix up rhombuses, rectangles and squares later.
Try it in two minutes
- Draw an arrowhead and a pentagon on paper. Ask: which one has a dent?
- Draw diagonals in both and see which diagonal goes outside.
- Ask your child to name one shape with equal sides but unequal angles, and one with equal angles but unequal sides.
Try at home. Ask your child to find five regular and five irregular shapes around the house.
Exterior Angles of a Polygon
Part of: Polygons and angles
If you walk round a polygon, you turn a little at each corner. The angles you turn through are the exterior angles, and together they make one full turn of 360 degrees. In a regular polygon all exterior angles are equal, so each is 360 divided by the number of sides.
Why it matters. This fact lets children find unknown angles and the number of sides quickly, without drawing. It also shows that a big idea can be true for all polygons at once.
Try it in two minutes
- Mark a start line on the floor and walk around a square path, turning at each corner. Count the turns.
- Ask: how many degrees is one full turn? How much is each turn in the square?
- Repeat the idea for a path with 6 equal turns and ask for each turn.
Try at home. Ask your child to find each exterior angle of a regular polygon with 10 sides and then its interior angle.
Trapezium and Kite
Part of: Kinds of quadrilaterals
A trapezium has one pair of parallel sides. If the sides that are not parallel are equal, it is an isosceles trapezium. A kite has two pairs of equal sides which are neighbours, and its diagonals cross at right angles.
Why it matters. Naming shapes by their properties helps children describe shapes exactly, and to avoid saying 'it looks like a diamond'. These shapes also appear in design, kites, roofs and bridges.
Try it in two minutes
- Use two pencils as parallel sides and two straws as the other sides to make a trapezium.
- Make a kite shape with two long and two short sticks, joining equal sticks together.
- Ask: what stays the same and what changes when you move the sticks?
Try at home. Ask your child to find a trapezium or a kite shape in a picture, a window or a toy.
Properties of a Parallelogram
Part of: Kinds of quadrilaterals
A parallelogram is a four-sided shape whose opposite sides are parallel. Its opposite sides are equal, its opposite angles are equal, and any two neighbouring angles add up to 180 degrees. Its diagonals cut each other in half, but they are not always equal.
Why it matters. These properties let us find missing sides and angles without measuring. They also explain why a door frame can fold flat and why folding scissor lifts work.
Try it in two minutes
- Make a parallelogram with four straws joined at the corners. Tilt it and watch which angles grow and which shrink.
- Ask: which angle is always the same as the opposite one? Which two add up to a straight line?
- Use two strips of paper to mark the diagonals and see where they cross.
Try at home. Ask your child to draw a parallelogram, measure the angles with a protractor and check the rules.
Rhombus, Rectangle and Square
Part of: Kinds of quadrilaterals
A rhombus is a parallelogram with four equal sides. Its diagonals cross at right angles and cut each other in half. A rectangle is a parallelogram with four right angles, and its diagonals are equal. A square is a rectangle with equal sides, so it has all these properties.
Why it matters. Seeing shapes as families helps children reason: if a shape is a square, they can use every fact about rectangles, rhombuses and parallelograms as well.
Try it in two minutes
- Fold a square sheet along both diagonals and check the angle at the centre with a corner of a book.
- Cut a rectangle and fold its diagonals to see if they are equal.
- Ask: what is the same and what is different between a rectangle and a square?
Try at home. Ask your child to draw a rectangle that is not a square and a rhombus that is not a square.
What your child will practise
- Convex, Concave and Regular Polygons: Lab Explorer Sort (Sort It Out)
- Exterior Angles of a Polygon: Number Quest (Collect the Answer)
- Properties of a Parallelogram: Space Puzzle (Clue Puzzle)
- Rhombus, Rectangle and Square: Candy Quick Fire (Quick Fire)
- Trapezium and Kite: Desert Quick Fire (Quick Fire)
- Quiz: Convex, Concave and Regular Polygons (8 questions)
- Quiz: Exterior Angles of a Polygon (8 questions)
- Quiz: Properties of a Parallelogram (8 questions)
- Quiz: Rhombus, Rectangle and Square (8 questions)