nce of triangles: Two ∆’s are congruent if sides and angles of a triangle are equal to the corresponding sides and angles of the other ∆.  In Congruent Triangles corresponding parts are always equal and we write it in short CPCT i E, corresponding parts of Congruent Triangles.  It is necessary to write a correspondence of vertices correctly for writing the congruence of triangles in symbolic FORM. CRITERIA for congruence of triangles: There are 4 criteria for congruence of triangles. SAS( side angle side): Two Triangles are congruent if two sides and the included angle of a triangle are equal to the two sides and included angle of the the other triangle. ---------------------------------------------------------------------------------------------------- Solution:  First show that ΔABC ≅ ΔADE by using SAS rule and then use  CPCT  to show given RESULT.  Given, AC = AE, AB = AD and ∠BAD = ∠EAC To prove:  BC = DE   Proof: We have ∠BAD = ∠EAC (Adding ∠DAC to both sides) ∠BAD + ∠DAC = ∠EAC + ∠DAC ⇒ ∠BAC = ∠EAD  In ΔABC and ΔADE, AC = AE (Given) ∠BAC = ∠EAD                    (proved above) AB = AD                                   (Given) Hence, ΔABC ≅ ΔADE             (by SAS congruence rule) Then, BC = DE                                      ( by CPCT.)  =========================================================