a) Why is triangle OBG similar to triangle OTE?

Question

nerdyotter · Answer

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danjs · Answer

They will be similar when the corresponding sides of the triangles are in equal proportions...

danjs · Answer

$$\frac{ OB }{ OT }=\frac{ OG }{ OE } = \frac{ BG }{ TE }$$

danjs · Answer

Length of smaller triangle over big triangle length is always the same fraction

mathstudent55 · Answer

Segments BG and TE are shown to be parallel.
That makes angle OBG and OTE congruent, and also angles OGB and OET congruent (by corresponding angles of parallel lines and a transversal).
Since you have two triangles with two pairs of corresponding congruent angles, by AA Similarity, the triangles are similar.