Page 61 - Concepts of Reasoning-8

Worksheet-12.4

Properties of Different Quadrilaterals

1. State whether the following statements are true or false :
a. The opposite angles in a parallelogram are equal.
b. All the sides of a rhombus are equal.

c. In a rectangle, only two angles are 90°.
d. In a kite, the two pairs of opposite angles are equal.

2. Choose the correct answer for each of the following :
a. The quadrilateral in which only one pair of opposite sides is parallel but not equal is:

i. Trapezium ii. Rectangle iii. Rhombus iv. Square
b. The quadrilateral in which only one pair of opposite angles is equal is:
i. Square ii. Kite iii. Rhombus iv. Trapezium
c. The quadrilateral in which each angle is 90° and the diagonals are equal and bisect each other at
right angles is:

i. Kite ii. Rhombus iii. Square iv. Trapezium

3. Solve the following word problems :
Parallelogram
B C
a. ABCD is a parallelogram in which AB = 10 cm and its 50°
perimeter is 50 cm. Find the length of each side of the 30°
parallelogram.
E
b. In the adjoining parallelogram ABCD, ÐEBC = 50°, ÐABE =
30° and ÐAED = 60°. Calculate ÐBEC, ÐEDA, ÐBAE and 60°
ÐECD.
c. In a parallelogram ABCD, the diagonals intersect at O. If BO A D
= 6 cm and AO = 4 cm, find the measure of AC and BD.
Rhombus and Kite
a. ABCD is rhombus. If ÐBCA = 60°, Find ÐADC
b. The diagonals of a rhombus ABCD intersect at O. If AC = 6 cm and BD = 8 cm, find the length of its
sides.
c. ABCD is a rhombus. Diagonal AC measures 4x + 4 and diagonal BD measures 5x – 2. Find the
value of x and the measures of AC and BD.
Square and Rectangle
a. In a parallelogram ABCD, if ÐA is a right angle then find the measure of all the angles. Write what
kind of a quadrilateral it is.
b. ABCD is a rectangle. Diagonal AC measures 2x + 2 and diagonal BD measures 4x – 8. Find the
value of x and the measures of AC and BD.

61 Reasoning - 8