Class 9 Maths — Quadrilaterals

Use the properties of a parallelogram and the mid-point theorem.

Name: ________________________

Before you start

A parallelogram with one diagonal drawn across it. Find the two pieces the diagonal makes, and the diagonal itself.

1. One of the two triangles
2. The other triangle — the same size and shape, turned round
3. The diagonal that makes them

Turn either triangle half a turn about the middle of the diagonal and it lands exactly on the other one. Opposite sides equal and opposite angles equal both fall straight out of that single fact.

1.One angle of a parallelogram is 65°. How big is the angle next to it, in degrees?
2.The four angles of any quadrilateral add up to how many degrees?
3.Which of these is true of every rhombus but not of every parallelogram?
- a) Opposite sides are parallel
- b) All four sides are equal
- c) Opposite angles are equal
- d) The diagonals cut each other in half
4.A quadrilateral has diagonals that are equal and cut each other in half at right angles. What is its most specific name?
- a) rhombus
- b) square
- c) rectangle
- d) parallelogram
5.One side of a parallelogram is 8 cm long. How long is the side opposite it, in centimetres?
6.The diagonals of a parallelogram cut each other in half. One diagonal is 14 cm long. How long is each of its two halves, in centimetres?
7.In triangle ABC, D is the mid-point of AB and E is the mid-point of AC. BC is 12 cm long. How long is DE, in centimetres?
8.The mid-point theorem says the segment joining the mid-points of two sides of a triangle is...
- a) twice the length of the third side
- b) perpendicular to the third side
- c) parallel to the third side and half its length
- d) equal in length to the third side

Answer key — Class 9 Maths — Quadrilaterals

1. 115
2. 360
3. b) All four sides are equal
4. b) square
5. 8
6. 7
7. 6
8. c) parallel to the third side and half its length