Question

given: ad ≅ cb, ∠dac ≅ ∠bca. prove: △adc ≅ △cba. look at the proof. name the postulate you would use to prove the triangles congruent. given: ad ≅ cb, ∠dac ≅ ∠bca. prove: △adc ≅ △cba. ad ≅ cb given. ∠dac ≅ ∠bca given. △adc ≅ △cba? ac ≅ ac reflexive property of congruence. aaa postulate. sas postulate. sss postulate.

Explanation:

Step1: Recall congruence postulates

There are several postulates to prove triangle - congruence: AAA (angle - angle - angle), SAS (side - angle - side), SSS (side - side - side).

Step2: Analyze given information

We are given $AD\cong CB$ (a side), $\angle DAC\cong\angle BCA$ (an angle), and $AC\cong AC$ (a side) by the reflexive property of congruence.

Step3: Identify the postulate

We have two sides and the included angle of one triangle congruent to two sides and the included angle of the other triangle. This is the SAS (Side - Angle - Side) postulate.

Answer:

B. SAS Postulate