Question

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

b:

c:

d:

Explanation:

Step1: Identify Reason A

Since the statement is “\(\angle ABC\) is a rt. \(\angle\)” and the reason is related to the given information about \(\angle ABC\) being a right - angle, the reason \(A\) is “given”.

Step2: Identify Statement B

By the definition of a right - angle (\(m\angle ABC = 90^{\circ}\)), so statement \(B\) is “\(m\angle ABC=90^{\circ}\)”.

Step3: Identify Reason C

Since \(\angle ABC=\angle ABD+\angle CBD\) (angle - addition postulate) and \(m\angle ABC = 90^{\circ}\), reason \(C\) is “angle - addition postulate”.

Step4: Identify Statement D

Combining \(m\angle CBD+m\angle CBD = 90^{\circ}\) (from step 6) using the addition property of like terms, we get \(2m\angle CBD=90^{\circ}\), so statement \(D\) is “\(2m\angle CBD = 90^{\circ}\)”.

Answer:

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