Question

Trapezoid A B C D is shown. Diagonals are drawn from point B to point D and from point A to point C and intersect at point E.
If quadrilateral ABCD is an isosceles trapezoid, which statements must be true? Select three options

BC ∥ AD
BD ⊥ AC
BA ≅ CD
BE ≅ ED
∠CBA ≅ ∠BCD

Answer 1

Correct choices:
- BC ∥ AD
- BA ≅ CD
- ∠CBA ≅ ∠BCD

Reason:
- In a trapezoid the two bases are parallel, so BC ∥ AD.
- "Isosceles" means the nonparallel sides (legs) are congruent, so BA ≅ CD.
- In an isosceles trapezoid the base angles are equal, so the angles at B and C (∠CBA and ∠BCD) are congruent.

The other two statements need not hold in general: the diagonals are not necessarily perpendicular, nor does their intersection bisect a diagonal.