Question

PLEASE HELP ME

Given: CA bisects angle, B, A, D∠BAD and start overline, A, D, end overline, \cong, start overline, A, B, end overline, .
AD ≅ AB


Prove: △ABC≅△ADC.

Answer 1

Triangles ABC and ADC are proven to be congruent using the Angle-Side-Angle (ASA) congruence postulate, based on the information that CA bisects ∠BAD and that AD is congruent to AB, with AC being a common side.

Step-by-step explanation:

To prove that triangles △ABC and △ADC are congruent, we can use the Angle-Side-Angle (ASA) congruence postulate. Given that CA bisects ∠BAD, it means that ∠BAC and ∠CAD are congruent. Also, since AD is congruent to AB, and AC is common to both triangles, we have two angles and the included side in common, satisfying the ASA condition.

Following the steps:

1. ∠BAC ≅ ∠CAD (CA bisects ∠BAD).
2. AD ≅ AB (given).
3. AC ≅ AC (common side).

By ASA postulate, we have △ABC ≅ △ADC.