Question

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.

Answer 1

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.