Question

In Fig. 4.60, check whether AD is the bisector of ∠A of ∆ABC in each of the following:

(i) AB = 5 cm, AC = 10 cm, BD = 1.5 cm and CD = 3.5 cm

(ii) AB = 4 cm, AC = 6 cm, BD = 1.6 cm and CD = 2.4 cm.

Answer 1

SOLUTION :  

(i) Given : AB = 5 cm, AC = 10cm, BD = 1.5 cm and CD = 3.5 cm

First check proportional ratio between sides.

Now,

AB/AC= 5/10 = 1/2

BD/CD =1.5/3.5 = 3/7

Here, AB/AC ≠ BD/CD

[If a line through one vertex of a triangle divides the opposite sides in the ratio of other two sides, then the line bisects the angle at the vertex.]

Hence, AD is not the bisector of ∠ A.

(ii) GIVEN : AB = 4 cm, AC = 6 cm, BD = 1.6 cm and CD = 2.4 cm.

First check proportional ratio between sides.

So,  AB/AC = BD/DC

4/6 = 1.6/2.4

⅔ = 2/3    

Here, AB/AC =  BD/CD

[If a line through one vertex of a triangle divides the opposite sides in the ratio of other two sides, then the line bisects the angle at the vertex.]

Hence, AD is the bisector of ∠ A.

HOPE THIS ANSWER WILL HELP YOU..

Answer 2

Answer:

SOLUTION :  

(i) Given : AB = 5 cm, AC = 10cm, BD = 1.5 cm and CD = 3.5 cm

First check proportional ratio between sides.

Now,

AB/AC= 5/10 = 1/2

BD/CD =1.5/3.5 = 3/7

Here, AB/AC ≠ BD/CD

[If a line through one vertex of a triangle divides the opposite sides in the ratio of other two sides, then the line bisects the angle at the vertex.]

Hence, AD is not the bisector of ∠ A.

(ii) GIVEN : AB = 4 cm, AC = 6 cm, BD = 1.6 cm and CD = 2.4 cm.

First check proportional ratio between sides.

So,  AB/AC = BD/DC

4/6 = 1.6/2.4

⅔ = 2/3    

Here, AB/AC =  BD/CD

[If a line through one vertex of a triangle divides the opposite sides in the ratio of other two sides, then the line bisects the angle at the vertex.]

Hence, AD is the bisector of ∠ A.

HOPE THIS ANSWER WILL HELP YOU..