Angle Bisector of a Triangle

Q.

Bisectors of the angles $B$ and $C$ of an isosceles triangle with $AB=AC$ intersect each other at $O.$ Show that external angle adjacent to $\angle ABC$ is equal to $\angle BOC$.

Q.

The internal bisectors of the angles B and C of a triangle ABC meet at O. Then, $\angle$BOC is equal to

1. 90° + A

2. 2A

3. 90° + ½ A

4. 180° – A

Q.

In the given figure, AB = AC. OB and OC bisect $\angle \text{ABC}$ and $\angle \text{ACB}$ respectively. If $\angle \text{BAC}={40}^{\circ }$, then $\angle \text{BOC}=$ ___

1. ${110}^{\circ }$

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

3. ${140}^{\circ }$

4. ${155}^{\circ }$

Q. $RA$ is the bisector of an angle of equilateral triangle $PQR$, then $\angle ARQ=$

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${20}^{\circ }$

Q. In the figure given above, what do AD, BF and CE represent?

1. Median
2. Altitude
3. Angle bisector
4. Perpendicular bisector

Q. In any triangle, a line from a vertex to its opposite side, bisecting the interior angle at that vertex is called -

1. Median
2. Altitude
3. Angle bisector
4. Perpendicular bisector

Q.

If two sides of a triangle are equal , then it has _____ equal angles.

1. Scalene triangle

2. Isosceles triangle

3. Equilateral triangle

4. Both A & C

Q. In an equilateral triangle ΔABC, AE is the angle bisector of ∠A, then the measure of ∠BAE is degrees.

Q. How many interior angle bisectors are there in a triangle?

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

Q. In the given Δ ABC, AB = AC. The angle bisector of ∠A meets the side BC at the point E.
The measure of ∠BAE$ is degrees.

Q. In the adjoining figure DE is internal bisector of $\angle D$, find the measure of $\angle x$.

1. ${155}^o$
2. ${105}^o$
3. ${115}^o$
4. ${130}^o$

Q. Construct $△ABC$ in which $BC=7cm,\angle B={75}^o$ and $AB+AC=12cm$

Q. Examine whether you can construct $\Delta$ DEF such that EF$=7.2$ cm, m$\angle$E$={110}^o$ and m$\angle$F$={80}^o$. Justify your answer.

Q.

Find the measure of $\angle DAE$ in the figure below.

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

2. ${30}^{\circ }$

3. $5^{\circ }$

4. ${15}^{\circ }$

Q. In the adjoining figure, which of the following are the interior angle bisectors? Check all that apply.

1. $AE$
2. $BF$
3. $PM$
4. $PN$

Q.

In the following figure, OB and OC are the angle bisectors. Find $\angle BOC$

1. ${90}^{\circ }$

2. ${100}^{\circ }$

3. ${80}^{\circ }$

4. ${110}^{\circ }$

Q. In the given figure, AB || CD, AB = 7 cm, BD = 25 cm and CD = 17 cm. Find the length of side BC(cm).

Q. A park, in the shape of a quadrilateral $ABCD$, has $\angle C={90}^o,AB=9m,BC=12m,CD=5m,AD=8m$. How much area does it occupy?( Write the first digit before decimal point)