S.chand Class 8 Maths Solution Chapter 13 Parallelograms Exercise 13 B

 Exercise 13 B

Question 1

1. For each of the statements given below, indicate if it is true (T) or false $(F)$ :

(a) A rectangle is a parallelogram.

(b) A square is a rectangle.

(c) A parallelogram is a rhombus.

(d) A square is a rhombus.

(e) A rectangle is a square.

(f) A square is a parallelogram.

2. What kind of quadrilateral is formed when the mid points of the sides of the following are joined?

(a) a rectangle,

(b) a rhombus,

(c) a kite,

(d) an isosceles trapezium.

3. $A B C D$ is a rectangle, $E F G H$ is a rhombus and $P Q R S$ is a square.

Complete the followings :

(i) $F H \perp$ ___

(ii) $G E$ bisects ___

(iii) If $\angle F E H=130^{\circ}, \angle E H G=$ ___

(iv) If $A C=4, B D=$ ___

(v) If PQ=4, PS=___

(vi) If $\angle E H G=48^{\circ}, \angle H G O=$ ___

(vii) If $H E=12, G H=$ ___

(viii) $\angle E O F=$ ___

4. The diagonals of a rectangle $A B C D$ intersect at $O$. If $\angle B O C=44^{\circ}$, find $\angle O A D$.

5. $A B C D$ is a rhombus with $\angle A B C=56^{\circ}$. Determine $\angle C A D$.

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6. $A B C D$ is a rhombus. If $\angle D A C=50^{\circ}$, find 

(a) $\angle A C D$

(b) $\angle C A B$

(c) $\angle A B C$.

7. $A B C D$ is a trapezium in which $A B \| D C$. If $\angle A=\angle B=40^{\circ}$, what are the measures of the other two angles?

8. Calculate the angles marked with small letters in the following diagrams.

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9. $A B C D$ is a kite. If $\angle B C D=40^{\circ}$, find (a) $\angle B D C$ (b) $\angle A B C$.

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10. $A B C D$ is a trapezium and $A B E D$ is a square. If $B E=E C$, find: (a) $\angle B A E$

(b) $\angle A B C$

(c) What shape is the figure $A B C E$ ?

11. $A B C D$ is a square and $A B R S$ is a rhombus. If $\angle S A D=120^{\circ}$, find: (a) $\angle A S D \quad$ (b) $\angle S R B$.

12. $A B C D$ is a kite and $\angle A=\angle C$. If $\angle C A D=70^{\circ}, \angle C B D=65^{\circ}$, find : (a) $\angle B C D$ (b) $\angle A D C$.

13. If the diagonals of a rhombus are $12 \mathrm{~cm}$ and $16 \mathrm{~cm}$, find the length of each side.

Multiple Choice Questions (MCQs)

14. What value of $x$ makes the given parallelogram a square ?

(a) $7.5^{\circ}$

(b) $6.5^{\circ}$

(c) $4.5^{\circ}$

(d) $8.5^{\circ}$

15. Quadrilateral $A B C D$ is a kite. What is the length of the line segment $A E$ ?

(a) $4 \mathrm{~cm}$

(b) $6 \mathrm{~cm}$

(c) $5 \mathrm{~cm}$

(d) $13 \mathrm{~cm}$

16.$C D E F$ is a square. Find $x$.

(a) $142^{\circ}$

(b) $92^{\circ}$

(c) $113^{\circ}$

(d) $83^{\circ}$