Georgia was shown two triangles that had one pair of congruent angles between two pairs of congruent sides. She preformed a series of rigid transformations in order to map one triangle perfectly on top of the other. What theorem has Georgia show to be true by doing these transformations?(1 point)

Question

Responses which answer is correct and why

the SAS congruence theorem
the SAS congruence theorem

the CPCTC congruence theorem
the CPCTC congruence theorem

the SSS congruence theorem
the SSS congruence theorem

the HL congruence theorem

Answer 1

The correct response is the SAS congruence theorem.

Explanation:

The SAS (Side-Angle-Side) congruence theorem states that if two triangles have a pair of congruent sides and the included angle between those sides is also congruent, then the triangles are congruent. In Georgia's case, she has two triangles with one pair of congruent angles between two pairs of congruent sides, which matches the condition required by the SAS theorem.

• CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is typically used after establishing congruence to prove that specific parts of the triangles correspond to each other.
• SSS (Side-Side-Side) congruence theorem applies when all three sides of one triangle are congruent to the three sides of another triangle.
• HL (Hypotenuse-Leg) congruence theorem is specifically for right triangles and involves the hypotenuse and one leg.

Since Georgia's situation fits the requirements of the SAS theorem, she has demonstrated the truth of the SAS congruence theorem through her series of rigid transformations.