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31 votes
Which measurements determine more than one triangle?

Which measurements determine more than one triangle?-example-1
User Marshalee
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1 Answer

16 votes
16 votes

Answer: Choice D

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Step-by-step explanation:

For any triangle, the three inside angles always add to 180 degrees.

For choice D we have 15+20+145 = 180, which shows that a triangle is possible here. In contrast, choice B isn't possible because 10+70+120 = 200.

Now for the angles mentioned in choice D, we can make infinitely many triangles of infinitely many sizes. The triangles are scaled copies of one another and they are similar triangles. There isn't enough information to pin down exactly one triangle.

This is why there isn't an AA (angle angle) theorem for congruences. Knowing just the angles isn't enough to uniquely determine a single triangle. We would have to know something at least one of the sides so we could either use ASA or SAS or SSS.

User Maschaub
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