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:

b:

c:

d:

Explanation:

Step1: Determine Reason A

The first statement is “\(\angle ABC\) is rt. \(\angle\)” and the reason is A. Since this is given in the problem (Given: \(\angle ABC\) is a right angle), the reason A should be "given".

Step2: Determine Statement B

The reason for statement B is "def. of rt. \(\angle\)". The definition of a right angle is that its measure is \(90^\circ\), so statement B should be \(m\angle ABC = 90^\circ\).

Step3: Determine Reason C

Statement 5 is \(m\angle ABD + m\angle CBD = 90^\circ\). From statement 3, we know \(m\angle ABC = 90^\circ\), and from the angle addition postulate, \(m\angle ABD + m\angle CBD = m\angle ABC\). So reason C is "angle addition postulate" (or "angle addition prop.").

Step4: Determine Statement D

Statement 6 is \(m\angle CBD + m\angle CBD = 90^\circ\) (from substitution, since \(m\angle ABD = m\angle CBD\)), and the reason for statement 7 is "add." (addition). So statement D should be \(2m\angle CBD = 90^\circ\) (adding \(m\angle CBD\) and \(m\angle CBD\) gives \(2m\angle CBD\)).

Answer:

A: given
B: \(m\angle ABC = 90^\circ\)
C: angle addition postulate (or angle addition prop.)
D: \(2m\angle CBD = 90^\circ\)