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 $\angle C A D$.
<fig>
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.
<fig>
9. $A B C D$ is a kite. If $\angle B C D=40^{\circ}$, find (a) $\angle B D C$ (b) $\angle A B C$.
<fig>
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) $83^{\circ}$
