Question 1172525: Please help
Seth is using the figure shown below to prove the Pythagorean Theorem using triangle similarity:
In the given triangle PQR, angle P is 90° and segment PS is perpendicular to segment QR.
The figure shows triangle PQR with right angle at P and segment PS. Point S is on side QR.
Part A: Identify a pair of similar triangles.
Part B: Explain how you know the triangles from Part A are similar.
Part C: If RS = 4 and RQ = 16, find the length of segment RP.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The altitude on hypotenuse theorem states that the right angle formed by PS divides the original triangle into triangles that are similar to each other and also to the original larger triangle that contains both.
Draw this and RS is to PS as PS is to 12 or SQ
that makes PS^2=48 and PS= 4 sqrt(3).
RQ is to PQ as PQ is to 12 or SQ
this is 16 is to PQ as PQ is to 12
PQ^2=192 and PQ is sqrt (192) or 8 sqrt (3)
The line PS is 4 sqrt(3) and these are all 30-60-90 right triangles.
that is one way to get the answer for RP, which is half the hypotenuse of the large triangle, or 8,
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the other way is that 16/RP =RP/4
RP^2=64, and RP=8.
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