Angie states the following:
"Given two triangles, if two pairs of corresponding sides and one pair of corresponding angles are congruent, then the triangles are congruent by Side-Angle-Side (SAS)."
-Which of the following options best describes Angie's statement?

A. Angie is correct since SAS requires two pairs of congruent sides and one pair of congruent angles.
B. Angie is incorrect since SAS is not a congruence criterion that can be used to prove that two triangles are congruent.
C. Angie is correct since any two pairs of congruent sides and any pair of congruent angles will satisfy the SAS congruence criterion.
D. Angie is incorrect since triangles with two pairs of congruent sides and one pair of congruent angles do not necessarily meet the SAS orientation.

The answer is letter D, Angie is incorrect since triangles with two pairs of congruent sides and one pair of congruent angles do not necessarily meet the SAS orientation.

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akposevictor akposevictor · Answer 2 · 2021-10-15T14:32:14+02:00

Based on the SAS congruence criterion, the statement that best describes Angie's statement is:

D. Two triangles having two pairs of congruent sides and a pair of congruent angles do not necessarily meet the SAS congruence criterion, therefore Angie is incorrect.

Recall:

The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.
An included angle is found between two sides that are under consideration.

See image attached below that demonstrates two triangles that are congruent by the SAS Congruence Theorem.

Thus, two triangles having two pairs of corresponding sides and one pair of corresponding angles that are congruent to each other is not enough justification for proving that the two triangles are congruent based on the SAS Congruence Theorem.

The one pair of corresponding angles that are congruent MUST be "INCLUDED ANGLES".

Therefore, based on the SAS congruence criterion, the statement that best describes Angie's statement is:

D. Two triangles having two pairs of congruent sides and a pair of congruent angles do not necessarily meet the SAS congruence criterion, therefore Angie is incorrect.

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