Page 164 - Maths Skills - 8

162 Maths

Rhombus
A rhombus is a parallelogram with four equal sides. In the fig. ABCD is a rhombus in which AB = BC = CD = DA.
In a rhombus, AB || DC and AD || BC. Here, HY ⊥ KS, K 2 5 Y

Properties of Rhombus ∠1 = ∠2 = ∠3 = ∠4, 1 6

In a rhombus, ∠5 = ∠6 = ∠7 = ∠8 X 90°
1. All the sides are equal. 2. The opposite sides are parallel. 8 7 4 3
3. The opposite angles are equal. 4. Diagonals are not equal. H S
5. The diagonals are perpendicular bisectors of each other.

6. The diagonals divide the rhombus into four congruent right triangles.

In the above figure quadrilateral KYSH is a rhombus. It is a parallelogram with four equal sides. In addition
to all the properties of a parallelogram, the diagonals are perpendicular and bisect the opposite angles.

At a Glance

S. No. Properties Parallelogram Rectangle Square Rhombus

1. Opposite sides are parallel. Yes Yes Yes Yes

2. Opposite sides are equal. Yes Yes Yes Yes
3. Adjacent sides are equal. No No Yes Yes

4. Opposite angles are equal. Yes Yes Yes Yes

5. All angles are right angle. No Yes Yes No

6. Diagonals are equal. No Yes Yes No

7. Diagonals bisect each other. Yes Yes Yes Yes

8. Diagonals bisect at right angles. No No Yes Yes

9. Diagonals bisect interior angles. No No Yes Yes

Trapezoid/Trapezium
A trapezoid is a quadrilateral with only one pair of parallel sides. The trapezoids are of following types:
(a) Scalene trapezoid: A scalene trapezoid is a trapezoid with no equal sides. W Z
In the figure below WXYZ is a scalene trapezoid in which WZ || XY.
It is shown in fig.
X Y
A D
(b) Right-angled trapezoid: A right-angled trapezoid is a trapezoid with two
right angles. In the figure below ABCD is a right-angled trapezoid in which
∠A = ∠B = 90° and AD || BC. It is shown in fig.
B C
P S

(c) Isosceles trapezoid: In an isosceles trapezoid, non-parallel sides are equal. In
the figure below PQRS is an isosceles trapezoid in which PS || QR and PQ = RS.
It is shown in fig. Q R