Question

patamon was given two generic triangles with one pair of congruent angles between two pairs of congruent sides. they show that a sequence of rigid transformations maps one triangle onto the other triangle such that the triangles overlap perfectly. what theorem has patamon justified through this process?
(1 point)
the cpctc theorem
the hl congruence theorem
the sas congruence theorem
the sss congruence theorem

Explanation:

• CPCTC Theorem: This theorem is about corresponding parts of congruent triangles being congruent. It is used after proving triangles congruent, not for proving the triangles congruent in the first place. So this is not the right choice.
• HL Congruence Theorem: This theorem is specific to right - angled triangles. It states that if the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, then the two right - triangles are congruent. Since the problem does not mention right - triangles, this is incorrect.
• SAS Congruence Theorem: The Side - Angle - Side (SAS) congruence theorem states that 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. The problem mentions “one pair of congruent angles between two pairs of congruent sides”, which is exactly the SAS condition.
• SSS Congruence Theorem: This theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. But the problem does not mention three sides, only two sides and an included angle.

Answer:

the SAS Congruence Theorem