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Example Questions
Example Question #1 : Acute / Obtuse Triangles
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)
Statement II only
Statement I only
Any of the three statements is enough to prove congruence.
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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