Isosceles Triangle and Its Properties

Q.

One of the base angles of an isosceles triangle is equal to ${45}^{\circ }$. Find the vertex angle of the triangle.

1. ${53}^{\circ }$

2. ${54}^{\circ }$

3. ${74}^{\circ }$

4. ${76}^{\circ }$

Q.

In Fig. BM and DN are both perpendiculars to the segments AC and BM = DN. Prove that AC bisects BD [3 MARKS]

Q.

In the adjoining figure, the value of x is?

1. ${25}^{\circ }$

2. ${26}^{\circ }$

3. ${29}^{\circ }$

4. ${28}^{\circ }$

Q. Question 10
D is a point on side QR of $\Delta PQR$ such that $PD\perp QR$. Will it be correct to say that $\Delta PQD\sim \Delta RPD$? Why?

Q.

If two angles of a triangle are ${40}^{\circ },{40}^{\circ }$, then the orthocenter of the triangle will be

1. Inside the triangle

2. Outside the triangle

3. On the triangle

4. It will always be inside the triangle.

Q.

In the adjoining figure the value of x is:

1. ${25}^{\circ }$

2. ${26}^{\circ }$

3. ${28}^{\circ }$

4. ${29}^{\circ }$

Q.

If the angles of an isosceles triangle are in the ratio of 5 : 2 : 2, then find the values of these angles.

1. , ,

2. , ,

3. , ,

4. , ,

Q. In figure, if $\angle D=\angle C$ then it is true that $\Delta ADE\sim \Delta ACB$, ? Why?

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

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

Q.

Which of the following figure are obtuse isosceles triangles?

AN 

Q. In an isosceles triangle, if the third angle is greater than or equal to ${80}^{\circ }$ then the maximum value each base angle can have is

1. ${100}^{\circ }$
2. ${50}^{\circ }$
3. ${40}^{\circ }$
4. ${80}^{\circ }$

Q.

In the given figure, BD = AD and DC = AC, If $\angle ABC={35}^{\circ },$ then $x^{\circ }$ = ___.

1. ${30}^{\circ }$

2. ${35}^{\circ }$

3. ${40}^{\circ }$

4. ${45}^{\circ }$

Q. Suppose ABC is an equiangular triangle . Prove that it is equilateral . ( You have seen earlier that an equilateral triangle is equiangular . is equivalent id equilaterality .

Q.

In $\Delta ABC$, AC $>$ AB and AD bisects $\angle A$. Which of the following option is correct?

1. ADC ADB

2. ADC ADB

3. ADC = ADB

4. None of these

Q.

One of the base angles of an isosceles triangle is equal to ${45}^{\circ }$. Find the vertex angle of the triangle.

1. ${53}^{\circ }$

2. ${76}^{\circ }$

3. ${54}^{\circ }$

4. ${74}^{\circ }$

Q.

In an isosceles triangle, if the base angles are equal, then ___ are equal.

1. all the sides

2. any two sides

3. sides opposite to these angles

4. none of the sides

Q.

In the figure given, if $\Delta ABC$ is an isosceles triangle and OB and OC are angle bisectors of $\angle B$ and $\angle C$ respectively, then $\Delta BOC$ is ____.

1. True

2. False

3. scalene
4. right-angled

Q. In the given figure, the value of 'x' and 'y' is:

1. $x={45}^{\circ },y={65}^{\circ }$
2. $x={125}^{\circ },y={65}^{\circ }$
3. $x={75}^{\circ },y={45}^{\circ }$
4. $x={125}^{\circ },y={35}^{\circ }$

Q.

In $△ABC$, $AB=AC$ and $\angle B={40}^{\circ }$. What is the value of $\angle C$?​​​​​​​

1. 6m, equilateral triangle

2. 4 m, Isosceles triangle

3. 6 m, Isosceles triangle

4. 4 m, equilateral triangle

Q.

The vertical angle of the given isosceles triangle is angle

1. B

2. A

3. C

4. None of the above