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.

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lublana lublana · Answer 1 · 2019-07-15T07:21:16+02:00

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.