If quadrilateral abcd is an isosceles trapezoid, which statements must be true? check all that apply.

bc ∥ ad
bd ⊥ ac
ba ≅ cd
be ≅ ed
∠cba ≅ ∠bcd

The
first, we consider the trapezoid,ABCD

trapezoid  must have two parallel lines, as we see on the graph, BC ∥ AD
so the first choice is true, plus BA ≅ CD

BD ⊥ AC is not true, in fact BD and AC are two secant lines 

let's consider BEC triangle, it is an isosceles, so 
BE ≅ EC, and ∠CBE ≅ ∠ECB

as for AED triangle, it is also an isosceles
AE ≅ ED, and ∠EAD ≅ ∠EDA

finally the true answers are 
BC ∥ AD
BA ≅ CD

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