Question

the sas congruence theorem quick check
what does the sas congruence theorem say? (1 point)
if two triangles have one pair of congruent angles and two pairs of congruent sides, then the triangles are congruent.
if two triangles have one pair of congruent angles and at least one pair of congruent sides, then the triangles are congruent.
if two triangles have one pair of congruent angles between two pairs of congruent sides, then the triangles are congruent.
if a triangle has an angle between two congruent sides, then it is isosceles.

Explanation:

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

• The first option is incorrect because it doesn't mention that the angle is between the two sides. Just having one pair of congruent angles and two pairs of congruent sides (without the angle being between the sides) is not sufficient for SAS.
• The second option is incorrect as having one pair of congruent angles and at least one pair of congruent sides is too vague. It doesn't meet the requirements of the SAS theorem which needs two sides and the included angle.
• The fourth option is about an isosceles triangle (a triangle with two congruent sides) and has nothing to do with triangle congruence via the SAS theorem.

Answer:

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