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.

Accepted Solution

Answer with  explanation:Given : [tex]m\angle AEB=45^{\circ}[/tex][tex]\angle AEC [/tex] is a right angle.[tex]\angle AEC=90^{\circ}[/tex]To prove that : Bisect [tex]\angle AEC[/tex]  .Proof: We are given that  [tex]m\angle AEB=45^{\circ}[/tex] [tex]\angle AEC=90^{\circ}[/tex]By definition of a right angle.[tex]\angle AEB+\angle BEC=90^{\circ}[/tex]45+[tex]\angle BEC=90[/tex]By substitution property [tex]\angle BEC=90-45[/tex]By subtraction property of equality[tex]\angle BEC=45^{\circ}[/tex]So, [tex]\angle BEC\cong \angle AEB[/tex]Because they have the same measure.Since BE divided the angle AEC into two congruent angles.Therefore, it is the angle bisector.Hence proved.