Question

in a triangleABC, AD is bisector of angleA. Prove that AB÷AC=BD÷DC​

Answer 1

Hi mate here is the answer:-✍️✍️

Question:

In ∆ABC, if AD is the bisector of ∠A, show that AB>BD and AC>DC

Answer:

Given:

∠BAD = ∠DAC

To prove:

AB>BD and AC>DC

Proof:

In ∆ACD,

∠ADB = ∠DAC + ∠ACD …exterior angle theorem

= ∠BAD + ∠ACD …

given that

∠BAD = ∠DAC∠ADB > ∠BAD

The side opposite to angle ∠ADB is the longest side in ∆ADB

So, AB > BD

Similarly in ∆ABD

∠ADC = ∠ABD + ∠BAD … exterior angle theorem

= ∠ABD + ∠CAD … given that ∠BAD = ∠DAC

∠ADC > ∠CAD

The side opposite to angle ∠ADC is the longest side in ∆ACD

So, AC > DC

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