# To prove: The congruency of /_RKM ~=/_OMK. Given information: The following information has been given /_MRK = /_KOM = 90^(circ) /_RKM=/_OMK KM is the common chord

To prove: The congruency of $\mathrm{△}RKM\stackrel{\sim }{=}\mathrm{△}OMK$.
Given information: The following information has been given
$\mathrm{\angle }MRK=\mathrm{\angle }KOM={90}^{\circ }$
$\mathrm{\angle }RKM=\mathrm{\angle }OMK$
KM is the common chord
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Formula used : By the virtue of similarity, if any two angles of the triangles are congruent, the third one will also be congruent
Proof : We know that in triangles RKM and OMK,
$\mathrm{\angle }MRK=\mathrm{\angle }KOM={90}^{\circ }$
$\mathrm{\angle }RKM=\mathrm{\angle }OMK$
KM is the common chord
Hence, by virtue of similarity,
$\mathrm{\angle }RMK=\mathrm{\angle }OKM$
Now, we can say that $\mathrm{△}RKM\stackrel{\sim }{=}\mathrm{△}OMK$ by SAS property of congruency
Hence, given congruency is proved