given: m∠aeb = 45°
∠aec is a right angle.
prove: bisects ∠aec.
proof:
we are given that m∠aeb = 45° and ∠aec is a right angle. the measure of ∠aec is 90° by the definition of a right angle. applying the gives m∠aeb + m∠bec = m∠aec. applying the substitution property gives 45° + m∠bec = 90°. the subtraction property can be used to find m∠bec = 45°, so ∠bec ≅ ∠aeb because they have the same measure. since divides ∠aec into two congruent angles, it is the angle bisector.