Sides opposite equal angles are Equal? Q Help

GRE Quant Problem Solving
1

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Hi All,

I understand there is a similarity going. BR is y/2 as Greg shows, BUT isnt there a rule that says sides opp equal angles are equal? PL correct me. I have used BR as y as it is opposite the same angle x, to which y is opposite!

Ty

2

I think you’re confusing equivalent with equal

3

Yes within a triangle equal angles have equal length, but for other triangles they are similar or lengths are in the same ratio