Question

Can someone help me please

Answer 1

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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 the segment from R is equal to the geometric mean of the two segments the other end is connected to.

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  segments PS and QS, gm RS

  segments PS and PQ, gm PR

  segments PQ and QS, gm QR