Question

determine which postulate/theorem proves the triangles are congruent (sss, sas, asa, aas, hl). if the triangles are not congruent, write “not congruent”. if the triangles are congruent, write the congruence statemer 24. postulate/theorem: ________________ △abc≅△______ 25. postulate/theorem: ______________ △abc≅△________

Explanation:

Step1: Analyze 24th problem

In $\triangle ABC$ and $\triangle CDA$, we have $\angle BAC=\angle DCA$ (alternate - interior angles), $AC = CA$ (common side), and $\angle BCA=\angle DAC$ (alternate - interior angles). By the ASA (Angle - Side - Angle) postulate, $\triangle ABC\cong\triangle CDA$.

Step2: Analyze 25th problem

In $\triangle ABC$ and $\triangle JPC$, we have $\angle A=\angle J$ (given), $\angle ACB=\angle JCP$ (vertical angles are equal), and $AC = JC$ (given). By the ASA (Angle - Side - Angle) postulate, $\triangle ABC\cong\triangle JPC$.

Answer:

1. Postulate/Theorem: ASA; $\triangle ABC\cong\triangle CDA$
2. Postulate/Theorem: ASA; $\triangle ABC\cong\triangle JPC$