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Answer:
{Segments, Geometric mean}
{PS and QS, RS}
{PS and PQ, PR}
{PQ and QS, QR}
Step-by-step explanation:
The three geometric mean relationships are derived from the similarity of the triangles the similarity proportions can be written 3 ways, each giving rise to one of the geometric mean relations.
short leg : long leg = SP/RS = RS/SQ ⇒ RS² = SP·SQ
short leg : hypotenuse = RP/PQ = PS/RP ⇒ RP² = PS·PQ
long leg : hypotenuse = RQ/QP = QS/RQ ⇒ RQ² = QS·QP
I find it easier to remember when I think of it as <em>the segment from R is equal to the geometric mean of the two segments the other end is connected to</em>.
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segments PS and QS, gm RS
segments PS and PQ, gm PR
segments PQ and QS, gm QR
