Question

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

Answer 1

Isosceles trapezoid has one pair of equal side and one pair of parallel side

For trapezoid ABCD, line AB equals to line CD and line AD is parallel to BC. The two diagonals, AC and BD, also has equal length. 

Angle BAD equals to angle ADC
Angle ABC equals to BCD

Point E, where the two diagonals intersect, isn't the middle point of the diagonals. 

Hence, from the options, the correct statements are
BC||AD
BA equals to CD
Angle CBA equals to angle BCD

Answer 2

The answer:
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