Question

3. in Fig. 6.15, Z POR = Z PRQ, then prove that
POS= PRT

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Answer 1

Answer:

Solution:

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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