Use the definition of an angle bisector, and use that CE is a common side for both triangles.
See solution.
Practice makes perfect
Let's begin with what we can determine by the fact that a line CE is dividing ∠BED into two congruent angles. By the definition of an angle bisector, we can determine that ∠BEC ≅ ∠DEC. We are also told that ∠BCE and ∠DCE are right angles. Let's mark the congruent angles on the given diagram.
Next, we will check for a common characteristic of both triangles. We notice that CE is a common side in both. Therefore, by the Reflexive Property of Congruent Segments we can determine that CE ≅ CE. Let's write what we now know.
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∠BEC ≅ ∠DEC & Angle
CE ≅ CE & Included Side
∠BCE ≅ ∠DCE & Angle
Considering these relationships, we can apply the Angle-Side-Angle (ASA) Congruence Postulate to conclude that △ ECB ≅ △ ECD.
Completed Proof
Given: & CE bisects ∠BED
& ∠BCE and ∠ECD are right angles
Prove: & △ ECB ≅ △ ECD
Proof: By the definition of an angle bisector, we have ∠BEC ≅ ∠DEC. Besides that, we are told that ∠BCE and ∠DCE are right angles, and so ∠BCE ≅ ∠DCE. Additionally, CE is a common side for both triangles, and by the Reflexive Property of Congruent Segments we have CE ≅ CE. Therefore, by the Angle-Side-Angle (ASA) Congruence Postulate we conclude that △ ECB ≅ △ ECD.
