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 sas congruence theorem
the hl congruence theorem
the cpctc theorem
the sss congruence theorem

Explanation:

• 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 triangles are congruent. Here, we have two pairs of congruent sides and one pair of congruent angles (the included angle between the two sides).
• HL Congruence Theorem: Applies only to right - angled triangles (hypotenuse - leg). There is no information that the triangles are right - angled.
• CPCTC Theorem: Stands for "Corresponding Parts of Congruent Triangles are Congruent". It is used to prove parts of triangles are congruent after proving the triangles are congruent, not to prove triangle congruence.
• SSS Congruence Theorem: Requires three pairs of congruent sides. Here we have only two pairs of congruent sides.

Answer:

the SAS Congruence Theorem