Question

Given that segment AD is congruent to segment BC, and angle DAB is congruent to CBA; Prove: triangle ABE is isosceles

Answer 1

Statement | Reason

AD ≅ BC | Given

∠DAB ≅ ∠CBA | Given

AB ≅ AB | Reflexive property of congruence

ΔADB ≅ ABC | SAS postulate

∠DBA ≅ ∠CAB | CPCTC

ΔABE is isosceles | Any triangle with 2 congruent angles is isosceles