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State if the following is true or false.

In the given figure, if PQ||RS, prove that $Δ P O Q ~ Δ S O R$

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True

False

answer is A.

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Detailed Solution

Given that PQ||RS.
Given figure is,

We know,
If the two lines are parallel to each other, then the alternative angles must be equal.
Consider the triangles

Δ P O Q

and

Δ S O R

.
As the angle POQ and SOQ are vertically opposite angles.
Therefore,

∠ P O Q = ∠ S O Q

As the line PQ and RS are parallel.
So, the alternate angles will be equal.
That is,

∠ P = ∠ S ∠ Q = ∠ R

Therefore, it can be said that the triangle

Δ P O Q

and

Δ S O R

are similar.
Therefore, the statement is true.
Option 1 is correct.

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