Triangle QRS is a right triangle. Complete the similarity statement. ΔSTR ~ Δ

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Question:

Triangle QRS is a right triangle. Complete the similarity statement. ΔSTR ~ ΔTQRRSTSQRRTQ

ΔSTR is similar to ΔRTQ

Step-by-step explanation:

Given QRS is a right angled triangle. we have to find the similarity statement ΔSTR ~ Δ__

Let ∠S=x

In ΔSTR, by angle sum property

∠S+∠STR+∠SRT=180°

∠SRT=90°-x

In ΔSRQ, by angle sum property

∠S+∠R+∠Q=180°

∠Q=90°-x

In ΔSTR and ΔRTQ

∠SRT=∠Q=90°-x     (proved above)

∠STR=∠RTQ           (each 90°)

RT=RT                      (common)

Hence, by AAS rule ΔSTR≅ΔRTQ

∴ ΔSTR is similar to ΔRTQ

Option 4 is correct.

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