Question

Create a two-column proof: given: e a b and d c b are two right triangles and ∠ b e d ≅ ∠ b d e . Point b is the midpoint of segment a c . Prove: △ e a b ≅ △ d c b

Answer 1

Using a two-column proof leveraging the HL Congruence Theorem and given information, we verify that right triangles △EAB and △DCB are congruent due to congruent hypotenuses and legs, stemming from the midpoint property and given angles.

Step-by-step explanation:

To prove that the right triangles △EAB and △DCB are congruent, we utilize a two-column proof with the given information. Since point B is the midpoint of segment AC, we know that AB = BC. We also have two pairs of congruent angles: ∠AEB and ∠BDC are right angles and ∠BED ≅ ∠BDE by the problem's statement. Therefore, by the HL (Hypotenuse-Leg) Congruence Theorem, wherein if the hypotenuse and one leg of a right triangle are congruent to the corresponding parts of another right triangle, the triangles are congruent, we have proved that △EAB ≅ △DCB.