Angle Bisector Theorem

Q. If in a triangle PQR, PQ = 4 cm , RP = 6 cm and PS is the angle bisector of the angle P with end S on the side QR, then QS : SR = .

1. 2 : 3
2. 4 : 5
3. 3 : 4

Q.

The perimeter of $△ABC$ is 49 cm. The angle bisector of $\angle A$ meets BC at M. BM = 6 cm, MC = 8 cm. Find AC.

1. 10 cm
2. 20 cm
3. 15 cm
4. 12 cm

Q. 5. If the bisector of any angle of a triangle also bisects the opposite side then prove that the triangle is an isosceles triangle. e bisector of any an

Q.

If the line through one vertex of the triangle internally divides the opposite side such that they are proportional to the sides containing the angle, then the line must bisect the vertex angle.

1. True

2. False

Q. In a ΔABC, if AB = AC and ∠B = 70°, find ∠A.

Q. The largest angle of a triangle, whose sides are 12, 18 and 20 inches, is bisected. Find the lengths of the segments created when the angle bisector intersects the opposite side of the triangle.

[ 2 marks ]

Q. The angle bisector of $\angle A$ divides the side BC of $△ABC$ in the ratio 2:3 and the area of $△ABD$ is 20 $c{m}^2$. Find the area of $△$ADC.

Q. The angle bisector of $\angle A$ divides the side BC of $△ABC$ in the ratio 3 : 5. The area of $△ABD$ = 15 $c{m}^2$. Area of $△$ADC =

1. 10 $c{m}^2$
2. 15 $c{m}^2$
3. 20 $c{m}^2$
4. 25 $c{m}^2$

Q. In the given figures, if AD, BE and CF are angle bisectors then match the correct pairs.

1. c × p = b × q
2. a × p = c × q
3. a × p = b × q

Q. If a line through ∠B divides the opposite side in proportion to the sides containing ∠B, then p : q = .

1. 1 : 1
2. 2 : 1
3. 1 : 2

Q.

The perimeter of $△ABC$ is 49 cm. The angle bisector of $\angle A$ meets BC at M. BM = 6 cm, MC = 8 cm. Find AC.

Q. If in the figure given above,
$\frac{AB}{BC}=\frac{AD}{DC}$,
then, the line p necessarily.

1. bisects ∠ B
2. bisects side AC
3. do not bisect ∠B

Q.
The line p cuts AB at O and bisects the angle C as shown. Therefore,
$\frac{AC}{BC}=$ .

1. $\frac{AO}{OB}$
2. $\frac{OB}{AO}$
3. $\frac{AO}{OC}$

Q. M is a point on side BC of a triangle ABC such that AM is the bisector of $\angle BAC.$ Is it true to say that perimeter of the triangle is greater than 2 AM? If True enter 1, else if False enter 0.

Q.

$\Delta DGH\text{and}\Delta DEF\text{are as shown below.}$ $\text{Find the lengths of segments DG and}\text{DE.}$
$\text{(All the measures are in cm.)}$

Q. The largest angle of a triangle, whose sides are 12, 18 and 20 inches, is bisected. Find the lengths of the segments created when the angle bisector intersects the opposite side of the triangle.

Q. In the given figure, if PS is an angle bisector, then
$\frac{RS}{SQ}=\frac{PR}{QP}$

1. False
2. True

Q.

In $△$ABC, AB = 3 and, AC = 4 cm and AD is the bisector of $\angle$A. Then, BD : DC is —

1. 9:16

2. 16:9

3. 3:4

4. 4:3

Q.

The largest angle of a triangle, whose sides are 12, 18 and 20 inches, is bisected. Find the lengths of the segments created when the angle bisector intersects the opposite side of the triangle.

1. 6 and 12 inches

2. 9 and 3 inches

3. 8 and 12 inches

4. 10 and 10 inches

Q.

The perimeter of $△ABC$ is 49 cm. The angle bisector of $\angle A$ meets BC at M. BM = 6 cm, MC = 8 cm. Find AB.

1. 20 cm

2. 22 cm

3. 15 cm

4. 12 cm