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7. In a square PQRS, PQ = (5a – 17) cm and QR = (2a + 4) cm. Find length of PS.

E
13
x
8. Let RICE is a rhombus. Find the value of x, y, and z. Also, find the perimeter R C
of the given rhombus. y O 12
5
z
I

R D

9. In rectangle READ, find ∠EAR and ∠RAD, if ∠ROE = 60°. 60° O

E A

B

10. In rhombus BEAM, find ∠AME and ∠AEM. E O M
70°

A
Construction of Different Quadrilaterals

At least five elements must be known to draw a unique quadrilateral. We can construct a unique
quadrilateral when the following measurements are given.

(a) When the measures of 4 sides and 1 diagonal are given.
(b) When the measures of 3 sides and 2 diagonals are given.

(c) When the measures of 2 adjacent sides and 3 angles are given.
(d) When the measures of 3 sides and 2 included angles are given.

(e) When the measures of 4 sides and 1 angle are given.
(f) When other special properties are known.

When Four Sides and a Diagonal are Given

Let us construct a quadrilateral ABCD, given that AB = 4.2 cm, BC = 3.7 cm,
CD = 2.9 cm, AD = 3 cm, and BD = 4.5 cm.
First, we should draw a rough sketch and mark the measurements of the sides and
diagonals as it will help us visualise the quadrilateral.
Steps of construction:

Step 1: Draw a line segment AB = 4.2 cm.
Step 2: With A as centre and radius = 3 cm, draw an arc.

Step 3: With B as centre and radius = 4.5 cm, draw an arc to intersect the
previous arc at D.

Step 4: Join AD and BD.

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