Page 187 - ICSE Math 8

8. PQRS is a rectangle. Diagonals PR and QS meet at point O. P Q
If OP = (2x + 4) units, OS = (3x + 1) units, find x and QS. 2x + 4
9. Identify all quadrilaterals that have.
(a) 4 sides of equal length 3x + 1 O

(b) 4 right angles
S R
Trapezium
A trapezium is a quadrilateral with at least one pair of parallel sides. P Q
In quadrilateral PQRS (Fig. 16.20), PQ || SR.
Thus, PQRS is a trapezium.
S R
Fig. 16.20

Types of trapezium
P Q
(a) Isosceles trapezium
A trapezium in which the non-parallel sides are equal is called
an isosceles trapezium. In trapezium PQRS (Fig. 16.21), S R
PQ || SR and PS = QR. Thus, it is an isosceles trapezium. Fig. 16.21

(b) Right trapezium P Q
A trapezium that has two right angles is a right trapezium. 90°
In trapezium PQRS (Fig. 16.22), –P = –S = 90º. Thus, it is a
right trapezium. 90°
S R
Fig. 16.22
P
Kite
A quadrilateral with two pairs of equal consecutive sides is known as a kite.
In quadrilateral PQRS (Fig. 16.23), PQ = PS and QR = SR. Thus, it is a kite. S O Q

Properties of a kite
(a) The diagonals intersect at right angles (PR ^ SQ).
(b) The longer diagonal bisects the shorter diagonal.
R
Example 10: Explain how KLMN is a trapezium. Which of its two sides are parallel? Fig. 16.23

Solution: In quadrilateral KLMN, N M
–L + –M = 100º + 80º = 180º 100°
But these are interior angles on the same side
of the transversal ML between the lines NM 80°
and KL. K L
fi NM || KL
Hence, KLMN is a trapezium. (One pair of opposite sides is parallel)

EXERCISE 16.4

R A

1. In the trapezium STAR given alongside, ST || RA. If ∠S = 50º
and ∠T = 50º, find the other two angles. 50° 50°
S T

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