Question

In Fig. 4.60, check whether AD is the bisector of ∠A of ΔABC 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
(iii) AB = 8 cm, AC = 24 cm, BD = 6 cm and BC = 24 cm
(iv) AB = 6 cm, AC = 8 cm, BD = 1.5 cm and CD = 2 cm
(v) AB = 5 cm, AC = 12 cm, BD = 2.5 cm and BC = 9 cm

Answer 1

Checked and found in which cases AD is the bisector of ∠A of ΔABC

Step-by-step explanation:

We need to checl  whether AD is the bisector of ∠A of ΔABC in each of the following case

as per angle bisector theorm

if AD is  the bisector of ∠A

then AB/BD  = AC/CD   or AB/AC = BD/CD

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

AB/AC = 1/2  

BD/CD  = 1.5/3.5 = 3/7

1/2 ≠ 3/7

AD is not the bisector of ∠A

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

AB/AC = 4/6   = 2/3

BD/CD  = 1.6/2.4 = 2/3

2/3 = 2/3

AD is  the bisector of ∠A

(iii) AB = 8 cm, AC = 24 cm, BD = 6 cm and BC = 24 cm

AB/AC =8/24 = 1/3

BD/CD  = 6/24 = 1/4

1/3≠ 1/4

AD is not the bisector of ∠A

(iv) AB = 6 cm, AC = 8 cm, BD = 1.5 cm and CD = 2 cm

AB/AC = 6/8   = 3/4

BD/CD  = 1.5/2 = 3/4

3/4 = 3/4

AD is  the bisector of ∠A

(v) AB = 5 cm, AC = 12 cm, BD = 2.5 cm and BC = 9 cm

AB/AC =5/12

CD = BC - BD = 9 - 2.5 = 6.5 cm

BD/CD  =2.5/6.5 = 5/13

5/12 ≠ 5/13

AD is not the bisector of ∠A

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