Question

what other information, if any, do you need to prove the two triangles congruent by sas? explain
choose the correct answer below
a (overline{gi}congoverline{nm}) is needed because the congruent angles need to be included between two corresponding congruent sides
b (overline{gi}congoverline{nm}) and (overline{gt}congoverline{nq}) are both needed because all three corresponding sides must be congruent
c (overline{gt}congoverline{nq}) 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:

The SAS (Side - Angle - Side) congruence criterion states that for two triangles to be congruent by SAS, two sides and the included angle of one triangle must be congruent to the corresponding two sides and included angle of the other triangle. In the given triangles, we already have one pair of sides congruent (marked with one tick) and one pair of angles congruent. We need another pair of sides such that the congruent angles are included between the two pairs of congruent sides. So, \(\overline{GT}\cong\overline{NQ}\) is needed because the congruent angles need to be included between two corresponding congruent sides.

Answer:

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