Question

what other information, if any, do you need to prove the two triangles congruent by sas? explain.

choose the correct answer below
a. (angle tcongangle mq) is needed because the congruent angles need to be included between two corresponding congruent sides.
b. (overline{gl}congoverline{nm}) and (angle tcongangle mq) are both needed because all three corresponding sides must be congruent.
c. (overline{gl}congoverline{nm}) is needed because the congruent angles need to be included between two corresponding congruent sides.
d. no additional information is needed to prove the triangles congruent by sas

Explanation:

For the SAS (Side - Angle - Side) congruence criterion, the angle must be included between the two sides. In the given triangles, we already have one pair of sides (the marked sides) and one pair of angles. To apply SAS, we need the other pair of sides adjacent to the given angles to be congruent. That is, \( \overline{IT}\cong\overline{MQ}\) (because the congruent angles \( \angle G\) and \( \angle N\) need to be included between two corresponding congruent sides).

Answer:

A. \( \overline{IT}\cong\overline{MQ}\) is needed because the congruent angles need to be included between two corresponding congruent sides.