Question

1. given: \\( \overline { a d } \cong \overline { c b } \\), \\( \angle d a c \cong \angle b c a \\) prove: \\( \triangle a d c \cong \triangle c b a \\) look at the proof. name the postulate you would use to prove the two triangles are congruent. given: \\( \overline { a d } \cong \overline { c b } \\), \\( \angle d a c \cong \angle b c a \\) prove: \\( \triangle a d c \cong \triangle c b a \\) sas postulate sss postulate aaa postulate

Explanation:

Step1: Recall congruence postulates

• SAS (Side - Angle - Side) Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
• SSS (Side - Side - Side) Postulate: If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
• AAA (Angle - Angle - Angle) Postulate: AAA does not prove triangle congruence (it proves similarity).

Step2: Analyze given information

• We are given that \(\overline{AD}\cong\overline{CB}\), \(\angle DAC\cong\angle BCA\), and \(\overline{AC}\cong\overline{AC}\) (reflexive property).
• The sides \(\overline{AD}\) and \(\overline{CB}\), the included angles \(\angle DAC\) and \(\angle BCA\), and the sides \(\overline{AC}\) and \(\overline{AC}\) satisfy the SAS postulate.

Answer:

SAS Postulate