Bonnie says that triangle PQR is congruent to triangle XYZ by Side-Angle-Side (SAS) Congruence Postulate, but Sasha says that there is not enough information to prove that the two given triangles are congruent. We want to know how is correct. To do so, we will analyze each opinion one at a time. Let's do it!
Is Bonnie Correct?
The diagram indicates two pairs of congruent sides and a congruent angle pair. However, the angle is not the included angle between the marked sides, so the Side-Angle-Side (SAS) Congruence Postulate does not apply.
Bonnie is not correct.
The triangles may be congruent, but SAS is not a correct justification.
Is Shada Correct?
The diagram below shows two triangles that are not congruent, but have two congruent pair of sides and the angle with the given measure at X and P.
We can see that although we have two congruent pair of sides, the triangles do not have the same shape and size. This example shows that there is not enough information on the given diagram to conclude congruence.
Shada is correct.
