PSAT Math : How to find if acute / obtuse triangles are congruent

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #231 : Plane Geometry

You are given triangles   and , with  and . Which of these statements, along with what you are given, is not enough to prove that ?

I)  and  have the same perimeter



Possible Answers:

None of these statements is enough to prove congruence.

Statement I only

Any of the three statements is enough to prove congruence.

Statement III only

Statement II only

Correct answer:

Statement III only


If  and  have the same perimeter, , and , it follows that . The three triangles have the same sidelengths, setting the conditions for the Side-Side-Side Congruence Postulate. 

If , then, since the sum of the degree measures of both triangles is the same (180 degrees), it follows that . Since  and  are congruent included angles of congruent sides, this sets the conditions for the SAS Congruence Postulate. 

In both of the above cases, it follows that .

However, similarly to the previous situation, if , then it follows that , meaning that we have congruent sides and congruent nonincluded angles. However, this is not sufficient to prove congruence.

"Statement III" is the correct response.

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