Question

In the given figure, AD/DB=
AE/EC
and angle ADE = angle ACB.
Prove that triangle ABC is an isosceles triangle.​

Answer 1

Answer:

AD/DB=AE/EC

So by using basic proportionality theorem

we get DE parallel to BC

So angle ADE is equal to angle DBC(corresponding angles)

and angle ADE is equal to angleECB

so angleABC is equal to angle ECB

So opposite angles are equal .So opposite sides are equal .There fore it is a isosceles triangle

Answer 2

Step-by-step explanation:

Given- In triangle ABC,

AB/DB=AE/EC and angle ADE=angle ACB.

To prove- ABC is isosceles triangle.

Const- -

Proof- AB/DB=AE/EC-(GIVEN)

DE||BC- (Converse of thales theorem)

angle ADE =angle ABC

(corresponding angles)

Then,angle ADB=ABC=ACB

angle ABC =angle ACB

Base angles are equal then AB=AC

So, triangle ABC is an isosceles triangle.