Question

Suppose TM is equal to GL and angle M is equal to angle G. What additional information is needed to prove triangle MTD is equal to triangle GLS by SAS?

a) The length of side TD should be equal to the length of side LS.

b) The measure of angle T should be equal to the measure of angle S.

c) The length of side MD should be equal to the length of side SL.

d) The measure of angle D should be equal to the measure of angle L.

Answer 1

To prove triangle MTD is congruent to triangle GLS by SAS, the required additional information is that the length of side TD should be equal to the length of side LS.

Step-by-step explanation:

To prove that triangle MTD is equal to triangle GLS by the SAS (Side-Angle-Side) criterion, we need to know two sides and the included angle are congruent between the triangles. We are given that TM is equal to GL and angle M is equal to angle G. To satisfy SAS, the additional piece of information required would be that either of the following pairs are equal:

• Side TD is equal to side LS (corresponding sides opposite the given angles), or
• Angle T is equal to angle S (included angles between the given pairs of sides).

Thus, the correct answer is: a) The length of side TD should be equal to the length of side LS. This, along with the given congruent sides and angles, would allow us to conclude the two triangles are congruent by the SAS postulate.