Quadrilaterals
Class 8 · Mathematics
5 ideas in Class 8 Mathematics, explained in plain words, with games and quizzes to practise.
Rectangles and Squares
A rectangle is a four-sided shape whose angles are all 90°. Its opposite sides are equal and parallel, and its diagonals are equal and cut each other in half. A square is a special rectangle with all sides equal, and its diagonals also cross at 90° and split the corner angles into two 45° parts. Every square is a rectangle, but a rectangle is not always a square.
Why it matters. Rectangles and squares appear in doors, books, tiles and fields. Knowing why the diagonals behave as they do helps children check shapes and build frames, and it prepares them for proving things in geometry.
Try it in two minutes
- Take two sticks of equal length and cross them at their middles. Ask your child to join the four ends with a thread and describe the shape (a rectangle).
- Now cross them at a right angle. What new thing is true? (all four sides are equal, so it is a square).
- Ask whether every square is a rectangle and why.
Try at home. Ask your child to measure the diagonals of a notebook, a window and a book cover and say what they notice.
The Angle Sum of a Quadrilateral
Draw one diagonal in a quadrilateral and it splits into two triangles. Each triangle has angles adding to 180°, so the four angles of the quadrilateral add to 180° + 180°, which is 360°. This is true for every quadrilateral. So if three angles are known, the fourth is 360° minus their sum.
Why it matters. This idea lets children find unknown angles without a protractor, and it explains why a quadrilateral cannot have exactly three right angles.
Try it in two minutes
- Draw any four-sided shape and add a diagonal. Count the two triangles.
- Tear off the four corners and place them together around a point. They fill the whole turn (360°).
- Ask: if three corners are 90°, what must the fourth be?
Try at home. Ask your child to draw three different quadrilaterals, measure all angles, and add them up.
Parallelograms and Their Properties
A parallelogram is a four-sided shape with both pairs of opposite sides parallel. Its opposite sides are equal and its opposite angles are equal, while two neighbouring angles add up to 180°. Its diagonals cut each other in half, but they are not usually equal. Rectangles and squares are special parallelograms.
Why it matters. Parallelograms show up in slanted frames, tiles and folding stands. Using their properties helps children find missing angles and lengths without measuring.
Try it in two minutes
- Make a parallelogram from four straws joined at the corners. Push it to slant it and compare opposite sides and angles.
- Ask: when one angle gets bigger, what happens to the neighbouring angle? (it gets smaller so that the two still add up to 180°).
- Ask whether the two diagonals look equal.
Try at home. Ask your child to draw a parallelogram with sides 5 cm and 3 cm, measure its angles, and check that neighbouring angles add up to 180°.
The Rhombus and Its Diagonals
A rhombus is a four-sided shape with all four sides equal. It is also a parallelogram, so opposite angles are equal and neighbouring angles add up to 180°. Its diagonals cut each other in half at right angles, and each diagonal divides the angles at its two ends into two equal parts. The diagonals of a rhombus are usually not equal.
Why it matters. Rhombus shapes appear in kites, tiles and the diamonds on playing cards. Their diagonal properties are useful for finding angles, and for telling a rhombus apart from a rectangle.
Try it in two minutes
- Cut a rhombus out of paper and fold it along each diagonal. The two halves match.
- Ask your child what angle the two fold lines make where they meet.
- Ask whether the two diagonals have the same length.
Try at home. Ask your child to draw a rhombus using a ruler and compass and test the diagonals with a set square.
Kites, Trapeziums and How Quadrilaterals Relate
A kite has two pairs of equal adjacent sides, and its diagonal along the line of symmetry cuts the other diagonal in half at 90°. A trapezium has at least one pair of parallel sides, and two angles on the same slanted side add up to 180°. In an isosceles trapezium the slanted sides are equal and the angles on the same parallel side are equal. Squares, rectangles and rhombuses are all parallelograms, and every parallelogram is a trapezium.
Why it matters. Sorting shapes into groups and knowing which are special cases of others is a key reasoning skill, and these shapes are common in design and building.
Try it in two minutes
- Show a paper kite and ask which sides are equal.
- Show a trapezoid-shaped object, such as a bag or a lamp shade, and ask which two sides look parallel.
- Ask: is a square also a kite? is a rectangle also a trapezium?
Try at home. Ask your child to draw a Venn-style picture of parallelograms, rectangles, rhombuses and squares.
What your child will practise
- Kites, Trapeziums and How Quadrilaterals Relate: Ocean Quick Fire (Quick Fire)
- Parallelograms and Their Properties: Space Puzzle (Clue Puzzle)
- Rectangles and Squares: Mission Control Quest (Collect the Answer)
- The Angle Sum of a Quadrilateral: Lab Explorer Quest (Collect the Answer)
- The Rhombus and Its Diagonals: Space Quick Fire (Quick Fire)
- Quiz: Kites, Trapeziums and How Quadrilaterals Relate (8 questions)
- Quiz: Parallelograms and Their Properties (8 questions)
- Quiz: Rectangles and Squares (8 questions)
- Quiz: The Angle Sum of a Quadrilateral (8 questions)