Question

PQR=PRQ then prove that PQS=PRT​

Answer 1

Answer:

PQR +∠PQS =180° (by Linear Pair axiom)

∠PQS =180°– ∠PQR — (i)

∠PRQ +∠PRT = 180° (by Linear Pair axiom)

∠PRT = 180° – ∠PRQ

∠PRQ=180°– ∠PQR — (ii)

[∠PQR = ∠PRQ]

From (i) and (ii)

∠PQS = ∠PRT = 180°– ∠PQR

∠PQS = ∠PRT

Hence, ∠PQS = ∠PRT

Step-by-step explanation:

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Answer 2

Answer:

hence proved

Step-by-step explanation:

ST is a straight line and sum of angle in linear pair always equal to 180

∠PQS + ∠PQR = 180° … (1)

And

∠PRT + ∠PRQ = 180° … (2)

From equation (1) and (2).we get:

∠PQS + ∠PQR = ∠PRT + ∠PRQ … (3)

But given that ∠PQR = ∠PRQ

Plug the value we get

∠PQS + ∠PRQ =∠PRT + ∠PRQ

∠PQS = ∠PRT + ∠PRQ - ∠PRQ

∠PQS = ∠PRT

Hence proved

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