College

Thank you for visiting Owen tex angle AEB 45 circ tex tex angle AEC tex is a right angle Prove tex EB tex bisects tex angle AEC tex Proof. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

Owen: [tex]\angle AEB = 45^\circ[/tex]
[tex]\angle AEC[/tex] is a right angle.

Prove: [tex]EB[/tex] bisects [tex]\angle AEC[/tex].

Proof:
We are given that [tex]m\angle AEB = 45^\circ[/tex] and [tex]\angle AEC[/tex] is a right angle.
The measure of [tex]\angle AEC[/tex] is [tex]90^\circ[/tex] by the definition of a right angle.

Applying the angle addition postulate gives:
[tex]m\angle AEB + m\angle BEC = m\angle AEC[/tex]

By substitution, we have:
[tex]45^\circ + m\angle BEC = 90^\circ[/tex]

Using the subtraction property, we find:
[tex]m\angle BEC = 45^\circ[/tex]

Thus, [tex]\angle BEC \cong \angle AEB[/tex] because they have the same measure.
Since [tex]EB[/tex] divides [tex]\angle AEC[/tex] into two congruent angles, it is the angle bisector.

Answer :

Answer:

Step-by-step explanation:

Certainly, let's analyze the given proof and see if it's valid.

Given:

* m∠AEB = 45°

* ∠AEC is a right angle

To Prove:

* EB bisects ∠AEC

Proof:

1. m∠AEC = 90° (Definition of a right angle)

2. m∠AEB + m∠BEC = m∠AEC (Angle Addition Postulate)

3. 45° + m∠BEC = 90° (Substitution Property, using m∠AEB = 45°)

4. m∠BEC = 45° (Subtraction Property of Equality)

5. ∠BEC ≅ ∠AEB (Definition of Congruent Angles: Angles with the same measure)

6. EB bisects ∠AEC (Definition of Angle Bisector: A ray that divides an angle into two congruent angles)

The proof is valid.

All the steps are logically sound and follow from the definitions and properties used.

Thank you for reading the article Owen tex angle AEB 45 circ tex tex angle AEC tex is a right angle Prove tex EB tex bisects tex angle AEC tex Proof. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!

Rewritten by : Jeany

Other Questions