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Prove that racRVRP = racVUPQ using the similarity riangle RVU ||| riangle RPQ.

Mathematics

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racRVRP = racVUPQ using the similarity riangle RVU ||| riangle RPQ

Step-by-step solution

3 steps
  1. Use the similarity from the previous question.

    From question 2.2.1, we proved that △RVU∣∣∣△RPQ\triangle RVU ||| \triangle RPQ.

  2. Write the ratios of corresponding sides for similar triangles.

    When two triangles are similar, the ratio of their corresponding sides is equal.
    For △RVU∣∣∣△RPQ\triangle RVU ||| \triangle RPQ:

    RVRP=VUPQ=RURQ\frac{RV}{RP} = \frac{VU}{PQ} = \frac{RU}{RQ}
  3. Select the required ratio.

    The question asks to prove RVRP=VUPQ\frac{RV}{RP} = \frac{VU}{PQ}. This is directly obtained from the ratios of corresponding sides.

    Therefore, RVRP=VUPQ\boxed{\frac{RV}{RP} = \frac{VU}{PQ}}.

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