Given: line AB_|_line BC, line DC_|_ line BS. Prove angle B is congruent to angle C

Question

Prove that angle B is congruent to angle C in 3 steps

Answer 1

The picture I have is a right angle ABC. The line BS lies in between lines AB and BC. The point D lies along BS so that when joined to point C DC is perpendicular to BS.

<ABS=90-SBC (because <ABC is a right angle and <ABC=90=ABS+SBC),

<DCB=90-SBC (because BDC is a right-angled triangle where D is the right angle so the other two angles must add up to 90 degrees to make up 180 degrees for the whole triangle),

therefore, <ABS=DCB.