Question

In a triangle ABC, AB = AC. Points E on AB and D on AC are such that AE = AD. Prove that triangles BCD and CBE are congruent.

Answer 1

Please refer the above photograph for the used process.

Hope this will be helping you!


KEY POINTS TO REMEMBER :-

☸️ Congruency Criteria :-

1⃣SAS (Side-Angle-Side): If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent.

2⃣SSS (Side-Side-Side): If three pairs of sides of two triangles are equal in length, then the triangles are congruent.

3⃣ASA (Angle-Side-Angle): If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent. 


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Answer 2

There are 4 ways by which we can prove any 2 triangles as congruent :

If they are having -

★ SSS : Side Side Side

Three pairs of side are equal then the triangles are congruent.

★ ASA : Angle Side Angle / AAS : Angle Angle Side

If any 2 pairs of angles and 1 side are equal then the triangles are congruent.

★ SAS : Side Angle Side

If any two pairs of sides and the included angle are equal then the triangles are congruent.

★ RHS : Right Hypotenuse Side

If any right angle triangles are having their hypotenuse and a pair of sides equal then they are congruent.