Question

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

TQR
RST
SQR
RTQ

Answer 1

RTQ

Explanation:

Let ∠S=a, In ΔSTR, using angle sum property, we have

∠S+∠STR+∠SRT=180°

⇒ ∠SRT=90°-a

Again In ΔSRQ, using angle sum property, we have

∠S+∠R+∠Q=180°

⇒ ∠Q=90°-a

Now, In ΔSTR and ΔRTQ

∠SRT=∠Q=90°-a (proved above)

∠STR=∠RTQ (each 90°)

RT=RT (common)

Hence, by AAS rule,

ΔSTR≅ΔRTQ

Thus, ΔSTR is similar to ΔRTQ

Option 4 is correct.

Answer 2

ΔSTR is similar to ΔRTQ

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.