Question

sche the following questions
i. In the adjoining figure,
If AB = 7 AC=9, BD=3.5 &CD=4.5
find whether ray AD is bisector of LA .???
plz send it fast..
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Answer 1

Here, we can see that  ∠BAC  is bisected by AD where AD touches BC at D.  BC=BD+DC where,  BC=3cm . We also have the values of adjacent sides  AB=6cm and  AC=5cm .

These satisfy the requirements of angle bisector theorem. Then, by the theorem, we have:

ABBD=ACDC  

⇒DC=AC∗BDAB=5∗36=2.5cm

Answer 2

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..