Question

identify the missing parts in the proof
given: \\( \angle a b c \\) is a right angle
\\( \overline { d b } \\) bisects \\( \angle a b c \\)
prove \\( m \angle c b d = 45 ^ { \circ } \\)
a
b
c
d
angle \\( a b c = 90 \\)
angle \\( a b d = 90 \\)
2 times the measure of angle \\( a b c = 90 \\)
2 times the measure of angle \\( c b d = 90 \\)

Explanation:

Step1: Analyze statement 1

Since \(\angle ABC\) is a right - angle, by the definition of a right - angle, \(m\angle ABC = 90^{\circ}\), so A is \(m\angle ABC=90^{\circ}\)

Step2: Analyze statement 3

By the definition of a right - angle (\(m\angle ABC = 90^{\circ}\))

Step3: Analyze statement 4

Since \(DB\) bisects \(\angle ABC\), by the definition of an angle bisector, \(m\angle ABD=m\angle CBD\)

Step4: Analyze statement 5

By the angle addition postulate (\(m\angle ABD + m\angle CBD=m\angle ABC\)), and since \(m\angle ABC = 90^{\circ}\), we have \(m\angle ABD + m\angle CBD=90^{\circ}\)

Step5: Analyze statement 7

From \(m\angle ABD + m\angle CBD=90^{\circ}\) and \(m\angle ABD=m\angle CBD\) (from step 4), substituting \(m\angle ABD\) with \(m\angle CBD\) gives \(m\angle CBD+m\angle CBD = 90^{\circ}\), or \(2\times m\angle CBD=90^{\circ}\)

Answer:

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