Question

In the given figure,
Angle Abe=Angle CBE and Angle ADE=angel cde. Prove that AD=CD​

Answer 1

Answer:

angle ADB= 180°- angle ADE.

angle CDB= 180°- angle CDE

=> angle CDB= 180°- angle ADE.

{since angle ADE = angle CDE}

Now, In triangle ADB and triangle CDB

angle ABD = angle CBD -----------(1)

(given)

angle ADB = angle CDB -----------(2)

(just solve above)

BD = BD ----------(3)

(common)

From eq. (1) ,(2) and (3) we get

triangle ADB is congruent to triangle CDE.

(by ASA congruency)

Hence, AD = CD

(by corresponding part of congruent triangle)