Question

identify the missing parts in the proof.
given: \\( \angle abc \\) is a right angle.
\\( \overline{db} \\) bisects \\( \angle abc \\).
prove: \\( m \angle cbd = 45 ^ { \circ } \\)
a:
\\( \checkmark \\)
b:
\\( \checkmark \\)
c:
\\( \checkmark \\)
d:
\\( \checkmark \\)

Explanation:

Step1: Identify the reason for statement 1

Since the problem states "Given: ∠ABC is a right angle", the reason for statement 1 (∠ABC is rt. ∠) is "given".

Step2: Determine statement B

By the definition of a right - angle (def. of rt. ∠), if ∠ABC is a right - angle, then \(m\angle ABC = 90^{\circ}\). So statement B is \(m\angle ABC=90^{\circ}\).

Step3: Find the reason for statement 5

Since \(m\angle ABC=m\angle ABD + m\angle CBD\) (angle - addition postulate) and \(m\angle ABC = 90^{\circ}\), the reason for \(m\angle ABD + m\angle CBD=90^{\circ}\) (statement 5) is "angle - addition postulate".

Step4: Calculate statement D

For \(m\angle CBD+m\angle CBD = 90^{\circ}\), using the addition property (add. prop.), \(2m\angle CBD=90^{\circ}\).

Answer:

A. given
B. \(m\angle ABC = 90^{\circ}\)
C. angle - addition postulate
D. \(2m\angle CBD=90^{\circ}\)