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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
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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