Question

D and E are points on the base BC of ΔABC such that AD=AE and ∠BAD=∠CAE. Prove that ΔABC is an isosceles triangle.

Answer 1

Answer:

first of all you have to see given

Given that: AD=AE,BD=EC

To prove: AB=AC

Since, AD=AE △ADE is an isosceles triangle.

AF⊥DE,DF=FE (Properties of isosceles triangle)

Now, BD+DF=FE+EC⇒BF=FC

In △AFB and △AFC,

⇒BF=FC

∠AFB=∠AFC

⇒AF is common side

Thus △AFB≅AFC

Therefore, AB=AC .....(By CPCT)

Step-by-step explanation:

thats yours answer