The SAS Congruence Theorem Quick Check

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Question
What does the SAS Congruence Theorem say?(1 point)
Responses

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 and at least one pair of congruent sides, then the triangles are congruent.

If a triangle has an angle between two congruent sides, then it is isosceles.
If a triangle has an angle between two congruent sides, then it is isosceles.

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

1 answer

The correct response regarding the SAS (Side-Angle-Side) Congruence Theorem is:

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

This means that if you have two triangles where two sides of one triangle are congruent to two sides of another triangle, and the angle between those two sides in each triangle is also congruent, then the two triangles are considered congruent.

None of the provided options perfectly match this statement, but the closest one is:

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

However, the phrase "one pair of congruent angles" does not correctly represent the SAS theorem, which emphasizes the side-angle-side relationship rather than angles alone. If you have to choose the best approximation, it's the third option, but be aware that it may not accurately convey the SAS theorem as originally defined.