Question

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

Answer 1

Answer: ΔPQS ≈ ΔPQR ≈ ΔPQS

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 ] .

Answer 2

With the given picture, we can evaluate and confirm that the first item in the choice is true which is below,
ΔPQR=ΔPSQ=ΔQSR
Since angle is the same for m∠PRQ is 90°, while for m∠PSQ and m∠QSR are also 90°.