Question

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

The answer is angel addition postulate

Explanation:

Answer 2

The proof is given below.

Explanation:

Given m∠AEB = 45° and ∠AEC is a right angle. we have to prove that EB divides ∠AEC into two congruent angles, it is the angle bisector.

Given ∠AEC=90° (Given)

∠AEC=∠AEB+∠BEC

⇒ 90° = 45° +∠BEC (Substitution Property)

By subtraction property of equality

⇒ ∠BEC = 90° - 45° = 45°

Hence, both angles becomes equal gives ∠AEB≅∠BEC

Since EB divides ∠AEC into two congruent angles, ∴ EB is the angle bisector.