Question

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what other information, if any, do you need to prove the two triangles congruent by sas? explain. choose the correct answer below. a. gl ≅ nm is needed because the congruent angles need to be included between two corresponding congruent sides. b. gt ≅ nq is needed because the congruent angles need to be included between two corresponding congruent sides. c. gt ≅ nq and gl ≅ nm are both needed because all three corresponding sides must be congruent. d. no additional information is needed to prove the triangles congruent by sas.

Explanation:

Step1: Recall SAS congruence criterion

The Side - Angle - Side (SAS) congruence criterion states that two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

Step2: Analyze given information

In \(\triangle GLT\) and \(\triangle NMQ\), we know that \(\angle T\cong\angle Q\) and \(LT\cong MQ\) (the single - tick marks indicate congruent sides). For SAS, we need the side adjacent to the given angle in each triangle to be congruent. That is, we need \(GT\cong NQ\) so that the congruent angles \(\angle T\) and \(\angle Q\) are the included angles between two corresponding congruent sides.

Answer:

B. \(GT\cong NQ\) is needed because the congruent angles need to be included between two corresponding congruent sides.