Which of the following similarity statements about the triangles in the figure are true?

ΔPQS ≈ ΔPQR ≈ ΔPQS    

Step-by-step explanation:

In the given picture we have a right triangle PQR inw hich SQ is perpendicular  to PR.

Then ΔPQS and ΔQRS are also right triangle.

Now, in ΔPQS and ΔPQR

∠PSQ=∠PQR [right angle]

∠P=∠P [common]

∴ΔPQS ≈ ΔPQR        [BY AA similarity ]                          → (1)

In ΔPQR and ΔPQR

∠RSQ=∠PQR [right angle]

∠R=∠R [common]

∴ΔPQR ≈ ΔPQR      [BY AA similarity ]                          → (2)

From (1) and (2), we have

    ΔPQS ≈ ΔPQR ≈ ΔPQS    

Because if two triangles is similar to one triangle then all three triangles are similar to each other  [BY AA similarity ]          .

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step-by-step explanation:

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