In the figure, triangle $OMN$ is a right-angled isosceles triangle, where $OM$ is perpendicular

Question

In the figure, triangle $OMN$ is a right-angled isosceles triangle, where $OM$ is perpendicular to $NM$ and $OM = NM$. Given that $OQ$ is parallel to $MN$ and $\angle POQ = \frac{1}{2} \angle QOM$, show that $P$, $O$, and $N$ lie on the same straight line. In the figure, triangle $OMN$ is a right-angled isosceles triangle, where $OM$ is perpendicular to $NM$ and $OM = NM$. Given that $P$ lies on $NO$ produced and $\angle POQ = \frac{1}{2} \angle QOM$, show that $OQ$ is parallel to $MN$.

Accepted Answer

(i) $P$, $O$, and $N$ are collinear (ii) $OQ\parallel MN$

Angles Formed by Two Parallel Lines and a Transversal

Angles Formed by Two Parallel Lines and a Transversal

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