Question

Identify the proof to show that Δabd≅Δcbd, where ∠bda≅∠bdc are right angles, d is the midpoint of ac, ab≅bc, and bd bisects ∠b.

Answer 1

By using the Side-Angle-Side (SAS) congruence theorem, we can establish that triangles ΔABD and ΔCBD are congruent since they have two congruent sides and the included right angle between them.

Step-by-step explanation:

To show that triangles ΔABD and ΔCBD are congruent, we need to prove that they satisfy the conditions of one of the congruence theorems. Since both ΔABD and ΔCBD have a right angle at points D (∠BDA ≅ ∠BDC), and it is given that AB ≅ BC and BD bisects ∠B, we have two congruent sides and the included angle (which is the right angle) being equal. Therefore, by the Side-Angle-Side (SAS) congruence theorem, we can conclude that ΔABD ≅ ΔCBD. Additionally, as D is the midpoint of AC, AD ≅ DC, which serves as the third pair of congruent sides, further solidifying our proof of congruence between the two triangles.