Question

# 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

Similarity
To prove:The congruency of $$\displaystyle\vec{{{S}{O}}}\stackrel{\sim}{=}\vec{{{T}{O}}}$$.
Given information: The following information has been given O is the center of the circle
$$\displaystyle\angle{S}{O}{V}=\angle{T}{O}{W}$$
$$\displaystyle\angle{W}{S}{O}=\angle{V}{T}{O}$$

2020-12-14
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
$$\displaystyle\vec{{{O}{W}}}=\vec{{{O}{V}}}={R}$$
Thus, now we can say that
$$\displaystyle\triangle{O}{W}{S}\stackrel{\sim}{=}\triangle{O}{V}{T}$$
Hence, for congruent triangles, we use virtue of congruency to tell us that
$$\displaystyle\vec{{{S}{O}}}\stackrel{\sim}{=}\vec{{{T}{O}}}$$
Hence, the given congruency is proved