Question

Question

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)
Responses which answer is correct and why a b c or d

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
the HL congruence theorem
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Answer 1

The correct response is the SAS congruence theorem.

Explanation: The SAS (Side-Angle-Side) congruence theorem states that if two triangles have one pair of congruent sides and the angle between those two sides is also congruent, then the two triangles are congruent. Georgia observed that she had one pair of congruent angles between two pairs of congruent sides, which matches the conditions of the SAS theorem.

The other options do not apply to the scenario described:

• CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is not a theorem about proving congruence but rather a step used after showing that two triangles are congruent.
• SSS (Side-Side-Side) congruence theorem requires all three sides of one triangle to be congruent to all three sides of another triangle, which is not the case here.
• HL (Hypotenuse-Leg) theorem applies specifically to right triangles and is not relevant to the given information.

Thus, the transformations performed by Georgia indicate that the triangles are congruent by the SAS theorem.