Question

Answer this question:

Your friend thinks that the triangles shown below are congruent by SAS. Is your friend​ correct? Explain.
Choose the correct answer below.
A.
​Yes, the figure indicates that three corresponding sides are congruent.
B.
​No, the congruent angles are not the included angles.
C.
​Yes, the figure indicates that two corresponding sides and their included angle are all congruent.
D.
​No, the congruent sides are not the included sides.
E.
​Yes, the figure indicates that two corresponding angles and their included side are all congruent.
F.
​No, the figure only indicates that two corresponding sides are​ congruent, not three as required by the SAS Postulate.

Answer 1

B. ​No, the congruent angles are not the included angles.

Explanation:

You want to know if the triangles shown are congruent by SAS.

SAS

The SAS congruence postulate tells you that two triangles are congruent if the angles between corresponding congruent sides are congruent. (The A=angle is between the S=side in SAS.)

In the diagrams, the marked angles are not between the marked sides. The SAS postulate cannot be used with these triangles.

In short, ...

No, the congruent angles are not the included angles

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Answer 2

B. ​No, the congruent angles are not the included angles.

Explanation:

The SAS (Side-Angle-Side) Postulate 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 triangles are congruent.

In the given figure, we can see that two sides of the two triangles are congruent: side AB is congruent to side DE, and side AC is congruent to side DF. However, the included angles, which are the angles formed by these sides, are not congruent. Angle BAC is not congruent to angle EDF.

Since the included angles are not congruent, we cannot use the SAS Postulate to conclude that the two triangles are congruent. Therefore, the correct answer is B: No, the congruent angles are not the included angles.