Question

Given: CA bisects BC, DA bisects DB, and BC is congruent to BD. Prove: Triangle CAB is congruent to Triangle DAB.

a. SSS (Side-Side-Side)
b. SAS (Side-Angle-Side)
c. ASA (Angle-Side-Angle)
d. AAS (Angle-Angle-Side)

Answer 1

To prove that Triangle CAB is congruent to Triangle DAB, we can use the ASA (Angle-Side-Angle) congruence criterion. Since CA bisects BC and DA bisects DB, we know that angles CAB and DAB are congruent. Additionally, BC is congruent to BD.

Step-by-step explanation:

To prove that Triangle CAB is congruent to Triangle DAB, we can use the ASA (Angle-Side-Angle) congruence criterion. Since CA bisects BC and DA bisects DB, we know that angles CAB and DAB are congruent. Additionally, BC is congruent to BD.

By SSS, we can prove that the sides AC and AD are congruent since BC is congruent to BD. Therefore, we have the angle-side-angle congruence which proves that Triangle CAB is congruent to Triangle DAB.