Identify the missing parts in the proof. Given: ∠ABC is a right angle.

DB bisects ∠ABC.

Prove: m∠CBD = 45°

A:

B:

C:

D:

A. Given

B.Measure of ABC=90

C.Angle addition Prostulate

D.2 times the measure of angle CBD=90

Step-by-step explanation:

The missing parts of the proof includes;

1) ∠ABC = m∠CBD + m∠ABD = 90° (Angle addition postulate)

2) m∠CBD = m∠ABD (Definition of angle bisector)

3) m∠CBD + m∠ABD  = m∠CBD + m∠CBD (Substitution property of equality)

Step-by-step explanation:

The given details of the proof are;

∠ABC is a right angle = 90°

Line DB is a bisector of ∠ABC

Therefore;

1) ∠ABC = m∠CBD + m∠ABD = 90° by angle addition postulate

By the definition of angle bisector, we have;

The angles formed by line DB from ∠ABC are equal,

2) m∠CBD = m∠ABD by the definition of angle bisector

3) m∠CBD + m∠ABD = 90° = m∠CBD + m∠CBD = 2 × m∠CBD by substitution property of equality

2 × m∠CBD = 90°

∴ m∠CBD = 90°/2 = 45°