What does the SAS congruence theorem state?

Question

A) If a triangle has an angle between two congruent sides, then it is isosceles
B) If two triangles have one pair of congruent angles between two pairs of congruent sides, then the triangles are congruent
C) If two triangles have one pair of congruent angles and at least one pair of congruent sides, then the triangles are congruent
D) If two triangles have one pair of congruent angles and two pairs of congruent sides, then the triangles are congruent

Answer 1

The SAS (Side-Angle-Side) congruence theorem states that if two triangles have two pairs of sides that are congruent and the angle included between those sides is also congruent, then the triangles are congruent. Based on the options provided, the correct statement that describes the SAS congruence theorem is:

B) If two triangles have one pair of congruent angles between two pairs of congruent sides, then the triangles are congruent.

(Note that this option is not the classic SAS statement but rather reflects an understanding of angle included within the context of congruency with regards to sides.)

For clarity, the classic SAS theorem can be summarized as: 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. However, if we are interpreting the options strictly, none perfectly align to the traditional SAS theorem's statement.