A quadrilateral is a plane shape with four sides and four interior angles.

They include:

a) Square

b) Rectangle

c) Parallelogram

d) Rhombus

e) Trapezium

The sum of the interior angles of a quadrilateral is 360º.

Properties of some quadrilaterals are given below.

 

a) Square

  (i) All sides are equal.

  (ii) Opposite sides are parallel.

  (iii) Each interior angle is equal to 90º.

  (iv) Diagonals are equal and bisect each other at 90º.

  (v) Diagonals bisect the interior angles.

b) Rectangle

  (i) Opposite side are equal and parallel.
  (ii) Each interior angle is equal to 90 degrees.
  (iii) Diagonals are equal and bisect each other.

 

c) Parallelogram

  (i) Opposite sides are equal and parallel.
  (ii) Opposite angles are equal.
  (iii) Diagonals bisect each other.
  (iv) Sum of adjacent angles is 180 degrees.

d) Rhombus

  (i) All sides are equal.
  (ii) Opposite sides are parallel.
  (iii) Opposite angles are equal.
  (iv) Diagonals bisect at 90 degrees.
  (v) Diagonals bisect the interior angles.

 

e) Trapezium

  (i) One pair of opposite sides is parallel.

Example 1;

Example 2;

Example 3;

KCPE Topical Questions

Class 6

Construction of Quadrilaterals

1. Line AB is one side of a quadrilateral ABCD. Complete the quadrilateral given that angle ABC = 120⁰ and lines BC = 7 cm, CD = 8 cm and AD = 9 cm. What is the size of the angle BCD?

A. 80⁰       B. 100⁰        C. 71⁰          D. 76⁰

 

2. In the figure below, the area of triangle PQR is equal to the area of triangle QRS. PQS is a straight line and Rn is the common height of the two triangles.

Which of the following must be true?

A. PQ = RS    B. QR =RS     C. QR = RS     D. PQ = QS

 

3. Line PQ below is one side of a quadrilateral PQRS. Complete the quadrilateral given that angle QPS = 70⁰, lines PS = 8 cm, SR = 7 cm and RQ = 10 cm.

What is the size of angle PSR?

A. 55⁰       B. 35⁰      C. 90⁰       D. 125⁰

 

4. The diagram below represents two sides of a quadrilateral ABCD. To locate point C of the quadrilateral, construct angle ADC = 60⁰ and the bisector of angle BAD. Join CB.

What is the size of angle ACB?

A. 136⁰        B. 55⁰        C. 106⁰         D. 74⁰

 

5. On the line YZ drawn below, construct triangle XYZ such that angle XYZ is 30⁰. Bisect angle YXZ and draw the bisector to meet line YZ at M.

What is the size of angle YMX?

A. 45⁰        B. 60⁰         C. 105⁰          D. 75⁰

 

6. On line Ab below, construct triangle ABC such that angle ABC = 90⁰ and line BC = 6 cm. Bisect angle BCA and the bisector meet AB at D.

What is the size of angle CDB?

A. 116⁰       B. 64⁰       C. 37⁰        D. 27⁰