Question

Decide whether triangles ABC and DEC are similar. Explain or show your reasoning.

Answer 1

AAA similarity

Explanation:

Similar triangles:

In ΔECD,

∠E + ∠D + ∠ECD = 180° {Angle sum property}

∠E + 36 + 123 = 180°

∠E + 159 = 180

∠E = 180 - 159

∠E = 21°

In ΔACB,

∠A + ∠B + ∠ACB = 180° {Angle sum property}

∠ACB + 36 + 21 = 180°

∠ACB + 57 = 180

∠ACB = 180 - 57

∠ACB= 123°

In ΔECD & ΔBCA,

∠A ≅ ∠D

∠B ≅ ∠A

∠BCA ≅ ∠ECA

ΔECD ~ ΔBCA by Angle Angle Angle similarity.