Given: Trapezoid ABCD, BC ǁ AD, EB=EC

Prove: ABCD is isosceles

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