9514 1404 393
Explanation:
There are several ways you can go at this. Here are a couple. All proofs will start with the given relations being repeated as part of the proof. Here are the next steps.
<h3>Angle Sum</h3>
∠AED ≅ ∠BAE . . . . alternate interior angles are congruent
∠AED +∠AEB = 90° . . . . angle sum theorem
∠BAE +∠AEB = 90° . . . . substitution property of equality
∠CEF ≅ ∠BCE . . . . alternate interior angles are congruent
∠CEF +∠CEB = 90° . . . . angle sum theorem
∠BCE +∠CEB = 90° . . . . substitution property of equality
∠BAE +∠AEB = ∠BCE +∠CEB . . . . substitution property of equality
∠BAE +∠AEB = ∠BCE +∠AEB . . . . substitution property of equality
∠BAE = ∠BCE . . . . addition property of equality
<h3>Congruent Triangles</h3>
∠ABE = ∠CBE = 90° . . . . BE ⊥ AC
BE ≅ BE . . . . reflexive property of congruence
ΔBEA ≅ ΔBEC . . . . ASA congruence theorem
∠BAE ≅ ∠BCE . . . . CPCTC