Question

in figure triangle PQR = triangle PRQ , then prove that traingle PQS = taringle PRT ​

Answer 1

As Given, ∠PQR=∠PRQ

To prove: ∠PQS=∠PRT

According to the question,

∠PQR+∠PQS=180

∘

∣ Linear Pair

⇒∠PQS=180

∘

−∠PQR--- (i)

Also ∠PRQ+∠PRT=180

∘

∣ Linear Pair

⇒PRT=180

∘

−∠PRQ

⇒∠PRQ=180

∘

−∠PQR−−−(ii)(∠PQR=∠PRQ)

From (i) and (ii),

∠PQS=∠PRT=180

∘

−∠PQR

∴∠PQS=∠PRT [hence proved]

Answer 2

Question :-

In figure, ∠PQR = ∠PRQ, then prove that ∠PQS = ∠PRT.

Answer :-

ST is a straight line.

∴ ∠PQR + ∠PQS = 180° …(1) [Linear pair]

Similarly, ∠PRT + ∠PRQ = 180° …(2) [Linear Pair]

From (1) and (2), we have

∠PQS + ∠PQR = ∠PRT + ∠PRQ

But ∠PQR = ∠PRQ [Given]

∴ ∠PQS = ∠PRT

Plz mrk as brainliest ❤