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svetoff
2 months ago
10

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. T

he 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.
Mathematics
2 answers:
Leona [12.6K]2 months ago
7 0

Response:

The evidence is detailed below.

Step-by-step reasoning:

Given ∠AEB=45° and ∠AEC is a right angle, thus ∠AEC=90°

we aim to demonstrate that EB serves as the angle bisector.

In the right triangle AEC,

∠AEC=90° while ∠AEB=45°

∵ ∠AEB+∠BEC=∠AEC

⇒ 45° + ∠BEC = 90°

By utilizing the subtraction property of equality

∠BEC = 45°

Thus,  ∠AEB = ∠BEC = 45°

The angle ∠AEB divides angle ∠AEC equally via the line segment EB confirming that EB is indeed the angle bisector of the angle ∠AEB.

AnnZ [12.3K]2 months ago
4 0
The solution to the query involves the angle Angle addition postulate. I trust this is helpful.
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Step-by-step explanation:

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