Step-by-step explanation:
1. ABCD is a trapezoid
We are given that ABCD is a trapezoid.
2. AD || BC
By definition of a trapezoid, one pair of opposite sides are parallel.
3. ∠ADE ≅ ∠CBD
Since AD and BC are parallel, the angles formed by the transversal line BD are congruent alternate interior angles.
4. ∠DAE ≅ ∠BCA
Line AC is also a transversal line, so the angles it forms with AD and BC are also alternate interior angles, which are congruent.
5. ΔAED ~ ΔCEB
Triangles AED and CEB share two pairs of congruent angles, so by AA similarity, they are similar.
