Question

triangle cde is an equilateral triangle ABCD is a square .show that triangle ade is congruent to triangle BCE

Answer 1

In Triangle ADE and BCE

DA is equal to CA (Triangle CDE is an equilateral triangle)
AD is equal to BC (sides of square is equal)
AE is equal to BE (Triangle AEB is an isosceles triangle so, sides opposite to opposite angles are equal)

Therefore, By S.S.S. Congruence rule Triangle ADE is congruent to Triangle BCE

Answer 2

CB = DA (All Sides of a square are equal)

CE = DE (Equilateral Triangle , Sides Are 60°)

∠EDA = ∠ECB [90°(All sides of square are 90°) + 60°(All sides of a Equilateral Triangle are 60°) =150°

Proved By SAS Congruency