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Alternate Interior Angles Theorem

Question 133I...

Question

Question 133

In the given figure, $Δ P Q R$ is the right-angled at P. U and T are the points on the line QR. If $Q P ∥ S T$ and $U S ∥ R P$ , find $∠ S$

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Solution

If $Q P ∥ S T$ and QT is a transversal, then $∠ P Q R = ∠ S T U$ [alternate interior angles]
and if $U S ∥ R P$ and QT is a transversal, then $∠ P R Q = ∠ S U T$ [alternate interior angles]
Hence, $∠ S$ must be equal to $∠ P$ i.e. $90^{\circ}$
Since two angles of triangle PQR is equal to the two angles of triangle STU .Hence their third angle will also be equal.

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Alternate Interior Angles Theorem

Standard VII Mathematics

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