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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.

User Mellie
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1 Answer

3 votes

Answer with explanation:

Given :
m\angle AEB=45^(\circ)


\angle AEC is a right angle.


\angle AEC=90^(\circ)

To prove that : Bisect
\angle AEC .

Proof: We are given that
m\angle AEB=45^(\circ)


\angle AEC=90^(\circ)

By definition of a right angle.


\angle AEB+\angle BEC=90^(\circ)

45+
\angle BEC=90

By substitution property


\angle BEC=90-45

By subtraction property of equality


\angle BEC=45^(\circ)

So,
\angle BEC\cong \angle AEB

Because they have the same measure.

Since BE divided the angle AEC into two congruent angles.Therefore, it is the angle bisector.

Hence proved.

User Manoj Shevate
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7.6k points