Page 165 - Maths Skills - 8

Understanding Quadrilaterals 163

Properties of Trapezoid

In an isosceles trapezoid,
1. The opposite non-parallel sides are congruent. 2. The bases are parallel.
3. The lower base angles are congruent. 4. The upper base angles are congruent.

5. The diagonals are congruent. 6. Any lower base angle is supplementary to any upper
base angle.

Kite
A quadrilateral is called a kite if it has two pairs of equal adjacent sides but T
unequal opposite sides. In the figure below, SPOT is a kite in which SP = ST
and OP = OT. S O
Properties of Kite

In a kite, P
1. Two disjoint pairs of consecutive sides are congruent by definition.
2. The diagonals are perpendicular.

3. One diagonal is the perpendicular bisector of the other.
4. One of the diagonals bisects a pair of opposite angles.

5. One pair of opposite angles are congruent.

Cyclic Quadrilateral
A quadrilateral with all its vertices on the circumference of a circle is called a cyclic A
quadrilateral. In the adjacent figure ABCD is a cyclic quadrilateral. D
Opposite angles in a cyclic quadrilateral are supplementary angles

i.e. ∠A + ∠C = 180° B

∠B + ∠D = 180°
C

Challenge
Observe the pattern given alongside:
State whether the given statement is false or true:

1. Every parallelogram is a square.

2. Every trapezium is a parallelogram.
3. Every square is a rectangle.

4. Every rectangle is a quadrilateral.
5. Every parallelogram is a trapezium.