Proving triangle similarity given QR PT and QPR STR prove PQR TSR

The triangles are right triangles, then we can apply Pytagoras´ theorem.

Solution is:

The triangles are similar

From the attached picture, and from parameterization concepts

RS = μ × RQ     0 < μ < 1

From Δ PRQ     sinα = RQ/PR               PQ = h₁ ( hypothenuse in Δ PRQ)

From Δ RST      sinα = RS/ST                ST = h₂ ( hypothenuse in Δ RST)

Then     RQ/h₁   = RS/h₂

or     RQ × h₂  =  RS × h₁      ⇒   h₂ = (RS/RQ) × h₁    ⇒ h₂ = μ × h₁

Then both hypothenuse are proportional, it follows both triangles are similar

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Here are the correct answers.

Step-by-step explanation:

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d. vertex

step-by-step explanation: