 # To prove:The congruency of vec(SO) ~= vec(TO). Given information: The following information has been given O is the center of the circle /_SOV = /_TOW /_WSO = /_VTO Line 2020-12-13 Answered
To prove:The congruency of $\stackrel{\to }{SO}\stackrel{\sim }{=}\stackrel{\to }{TO}$.
Given information: The following information has been given O is the center of the circle
$\mathrm{\angle }SOV=\mathrm{\angle }TOW$
$\mathrm{\angle }WSO=\mathrm{\angle }VTO$
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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 : From the given information we can say that by the virtue of similarity, triangles OWS and OVT are similar.
Now, we know that
$\stackrel{\to }{OW}=\stackrel{\to }{OV}=R$
Thus, now we can say that
$\mathrm{△}OWS\stackrel{\sim }{=}\mathrm{△}OVT$
Hence, for congruent triangles, we use virtue of congruency to tell us that
$\stackrel{\to }{SO}\stackrel{\sim }{=}\stackrel{\to }{TO}$
Hence, the given congruency is proved