Question

a) Why is triangle OBG similar to triangle OTE?

Answer 1

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

Answer 2

\[\frac{ OB }{ OT }=\frac{ OG }{ OE } = \frac{ BG }{ TE }\]

Answer 3

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

Answer 4

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.