Given: Trapezoid ABCD, BC ǁ AD, EB=EC

Prove: ABCD is isosceles

Given
∠EBC = ∠ECB
Substitution
∠EBC = ∠A and ∠ECB = ∠D
∠A = ∠D
BC ǁ AD, EB=EC
ABCD is isosceles
Definition
Parallel lines form equal corresponding angles
If two sides of a triangle are equal, the angles opposite them are equal