Question

Given: dc bisects ∠acb and ac≅bc. Prove: acd ≅ bcd.

Answer 1

Using the given information that dc bisects ∠ACB and AC ≡ BC, and knowing that DC is a shared side, we can conclude that △ACD ≡ △BCD by the SAS postulate.

Step-by-step explanation:

To prove that triangles ACD ≡ BCD, we need to use the given information that dc bisects ∠ACB and AC ≡ BC. The fact that dc bisects ∠ACB means that ∠ACD and ∠BCD are equal. Since side AC is congruent to side BC, and DC is shared between both triangles, we now have two sides and the included angle that are congruent, which satisfies the SAS (Side-Angle-Side) postulate for triangle congruence.

This can be summarized as:

1. AC ≡ BC (Given)
2. dc bisects ∠ACB, so ∠ACD = ∠BCD (Given)
3. DC is shared by both triangles ACD and BCD (Common side)
4. By the SAS postulate, △ACD ≡ △BCD