Question

Given:

segment AD is congruent to segment AB, segment AC bisects angle DAB
Prove: triangle ADС is congruent to triangle АВС

Answer 1

To prove triangle ADC is congruent to triangle ABC, we can use the Side-Angle-Side (SAS) congruence criterion.

Step-by-step explanation:

To prove that triangle ADC is congruent to triangle ABC, we can use the Side-Angle-Side (SAS) congruence criterion. Here's how:

1. Given: segment AD is congruent to segment AB, segment AC bisects angle DAB
2. Since segment AD is congruent to segment AB, we have AD = AB.
3. Since segment AC bisects angle DAB, we have angle CAD = angle CAB.
4. From steps 2 and 3, we have two congruent sides (AD = AB) and the included angle (angle CAD = angle CAB) which satisfies the SAS criterion.
5. Therefore, triangle ADC is congruent to triangle ABC.