Question

Q2. In triangle ABC, D and E are points on the sides BC such that CE= DB and angle AEC = angle ADB. Show that AED is an isosceles triangle and triangle CAD is congruent to triangle BAE​

Answer 1

Answer:

In triangle ADE , angle ADE = angle AED ( given ). [ If opposite angles in a triangle  are equal then opposite sides are equal. ]

Therefore , side AD = side AE ………………(1)

Let angle ADE = angle AED = t°. , then

Angle ADB = (180-t)° and angle AEC =(180-t)°

or, Angle ADB = angle AEC…………………..(2)

In ∆ABD and ∆ ACE.

Side BD = side CE. (given)

Side AD = side AE. ( proved above).

Angle ADB = angle AEC. ( proved above ).

Thus , ∆ ABD congruent ∆ ACE.

Hence , side AB = side AC . , or ∆ ABC is an isosceles triangle . Proved

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