Properties of isosceles triangle

Q.

$△ABC$ is an isosceles triangle and AB = AC. If side BA is produced to D such that BA = AD, what is the measure of $\angle DCB$?

1. ${60}^{\circ }$

2. ${90}^{\circ }$

3. ${120}^{\circ }$

4. ${30}^{\circ }$

Q.

From the given figure, what can be said about quadrilateral ABCD?

1. Rhombus

2. Parallelogram

3. Kite

4. Square

Q. In the adjoining figure the value of x is?

1. ${26}^{\circ }$
2. ${28}^{\circ }$
3. ${25}^{\circ }$
4. ${29}^{\circ }$

Q.

O is any point on the bisector of the acute angle $\angle$XYZ. From O, a line is extended to join XY such that OP is parallel to ZY. Then, $△$YPO is:

1. Equilateral

2. Scalene

3. Isosceles but not right angled

4. Right & isosceles

Q.

In $△ABC$, $\angle B=\angle C$ and $AB=1.5\left(BC\right)$. If perimeter of the triangle is 8 cm, then AC is equal to ______cm.

1. 2
2. 3
3. 1
4. 4