Question

In Fig. 10.25, AB = AC and DB = DC, find the ratio ∠ABD:∠ACD.

Answer 1

The ratio of ∠ABD : ∠ACD is 1 : 1.

Explanation:

Given data:

AB = AC and DB = DC

To find the ratio of ∠ABD : ∠ACD

In triangle ABC, AB = AC

So that ΔABC is an isosceles triangle.

In isosceles triangle, angles opposite to equal sides are equal.

⇒ ∠ABC = ∠ACB

In triangle DBC, DB = DC

So that ΔDBC is an isosceles triangle.

In isosceles triangle, angles opposite to equal sides are equal.

⇒ ∠DBC = ∠DCB

Consider  ∠ABD : ∠ACD

$\Rightarrow(\angle \mathrm{ABC}-\angle \mathrm{DBC}):(\angle \mathrm{ACB}-\angle \mathrm{DCB})$

$\Rightarrow(\angle \mathrm{ABC}-\angle \mathrm{DBC}):(\angle \mathrm{ABC}-\angle \mathrm{DBC})$ $[\because \angle A B C-\angle A C B \text { and } \angle D B C=\angle D C B]$

$\Rightarrow 1: 1$

$\therefore \angle \mathrm{ABD}: \angle \mathrm{ACD}=1: 1$

To learn more...

1. AB=AC & DB=DC,find the ratio of angle ABD : angle ACD

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2. In the given figure, AB =AC and DB = DC. Prove that ∠ABD=∠ACD

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Answer 2

Step-by-step explanation:

hope it will help u .......