Question

What additional information would you need to conclude that using the SAS Congruence Theorem?

A) The lengths of the sides of both triangles
B) The measures of the angles of both triangles
C) The measures of the included angles and one pair of corresponding sides of both triangles
D) The measures of the included angles of one triangle and the length of one side

Answer 1

You need the measures of the included angles and one pair of corresponding sides of both triangles to use the SAS Congruence Theorem, which states that two triangles are congruent if two sides and the included angle of one triangle are congruent to those of another.

Step-by-step explanation:

To conclude that two triangles are congruent using the SAS Congruence Theorem, you need to know three things about each of the triangles: two sides and the angle between them, also known as the included angle. Therefore, the answer to what additional information you would need is C) The measures of the included angles and one pair of corresponding sides of both triangles.

The SAS (Side-Angle-Side) Theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. The 'included angle' refers to the angle formed between the two known sides.