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OpenStudy (quickstudent):
question attached. my answer:
RA is twice as big as EA: 3.5 * 2 = 7
RA = 7
AH is twice as big as AC: 6 * 2 = 12
AH = 12
7/3.5 = 2
12/6 = 2
According to the SAS Similarity Postulate, the two triangles are similar, because two of their sides are proportional, and the included angles are both right angles, so they are congruent.
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OpenStudy (joannablackwelder):
I agree that the two triangles are similar, but not that they are congurent.
OpenStudy (joannablackwelder):
To be congruent, they have to have the same length of two sides and the included angle, not just proportional.
OpenStudy (quickstudent):
I meant that the angles were congruent, not the triangles.
OpenStudy (joannablackwelder):
Ah, I see what you mean. Yes, that is true. :-) And your side lengths are correct.