Question

"According to the diagram below, which similarity statements are true?

Answer 1

The answer is C. PQS ~ QRS
Since R of QRS is a right angle, and Q of PQS is also a right angle, they are similar.
Since S remains the same angle for both triangles and since Q and R are the same (90°), then the angles of P and R of PQS must be the same as well.
Thus, PQS ~ QRS

Answer 2

Answer: C. ΔPQS ~ ΔQRS

Step-by-step explanation:

In the given picture, we can see Δ PQS is a right triangle right angled at Q, with R as altitude.

Thus, Δ PQR and ΔQRS are right triangles right angles at R.

Now, In Δ PQS and ΔQRS

∠ PSQ=∠RSQ and ∠PQS=∠QRS → corresponding angles are equal

⇒ΔPQS ~ ΔQRS [by AA similarity criteria]

Rest of other options do not have corresponding angles congruent .