Given: m <AEB = 45° <AEC is a right angle. Prove: E 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 BLANK 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 EB divides <AEC into two congruent B A E angles, it is the angle bisector.