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

## Example Questions

### Example Question #1 : How To Find If Acute / Obtuse Triangles Are Congruent

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

II)

III)

Any of the three statements is enough to prove congruence.

Statement I only

Statement II only

None of these statements is enough to prove congruence.

Statement III only

Statement III only

Explanation:

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.