Question

In the given figure- OP||SR, OQ||ST. Show that

Answer 1

Answer:

with reference to OP perpendicular to SR and OQ perpendicular to ST u can show that are equal with angels

Answer 2

The angle ∠POQ is equal to ∠RST.

Given:

In the given figure - OP||SR, OQ||ST

To Find:

The angle ∠POQ is equal to ∠RST.

Solution:

We are required to show that the angle ∠POQ is equal to ∠RST.

To show that extend a line from SR to V connecting OQ at U.

Now from the picture given below

Considering the SU line segment has the intersection between the rays ST and OQ.

⇒ The angle ∠RUQ is equal to the angle ∠RST as the corresponding angles are equal.
∠RUQ = ∠RST  ------(1)

Now considering the OU line segment has the intersection between the rays OP and OQ.

⇒ The angle ∠POQ is equal to the angle ∠RUQ as the corresponding angles are equal.

∠POQ = ∠RUQ     ------(2)

From equation(1) and equation(2) we can show

∠POQ = ∠RST

Therefore, The angle ∠POQ is equal to ∠RST.

Hence shown.

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