Given: m∠AEB = 45°
∠AEC is a right angle.
Prove: Ray E B bisects ∠AEC.
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Mathematics, 30.12.2020 07:40 rebeckas0102
Given: m∠AEB = 45°
∠AEC is a right angle.
Prove: Ray E B bisects ∠AEC.
3 lines extend from point E. A horizontal line extends to the left to point A and a vertical line extends up to point C. Another line extends halfway between the other 2 lines to point B. Lines A E and E C form a right angle.
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 Ray E B divides ∠AEC into two congruent angles, it is the angle bisector.
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