Question

In a triangle ABC, AB = AC and A = 36º. If the internal bisector of 2C meets AB at point D, prove that AD = BC​

Answer 1

Given: ∠A=36° and AB=AC

Since, AB=AC

∠B=∠C=x (Isosceles triangle property)

In △ABC

∠A+∠B+∠C=180°

36+x+x=180°

x=72°

∠B=∠C=72°

Since, CD bisects ∠C

∠BCD=∠ACD= 1/2∠C=36°

Now, In △BDC,

∠B+∠BCD+∠BDC=180 (Angle sum property)

72+36+∠BDC=180°

∠BDC=72°

Thus, ∠BDC=∠B=72°

Hence, BC=AD (Isosceles triangle property)

Answer 2

Answer:

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Step-by-step explanation:

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