Question

writing a two - column proof
statements\treasons

1. ∠abc is rt. ∠\t1. a
2. db bisects ∠abc\t2. given
3. b\t3. def. of rt. ∠
4. m∠abd = m∠cbd\t4. def. of bis.
5. m∠abd + m∠cbd = 90°\t5. c
6. m∠cbd + m∠cbd = 90°\t6. subs. prop.
7. d\t7. add.
8. m∠cbd = 45°\t8. div. prop.

identify the missing parts in the proof.
given: ∠abc is a right angle.
db bisects ∠abc.
prove: m∠cbd = 45°
a:
b:
c:
d:

Explanation:

Step1: Define right - angle

A right - angle measures 90°. So, since $\angle ABC$ is a right - angle, $m\angle ABC = 90^{\circ}$. This should be the reason for statement 1, so A is "Given".

Step2: Write measure of right - angle

Statement 3 should be $m\angle ABC=90^{\circ}$ because of the definition of a right - angle. So B is $m\angle ABC = 90^{\circ}$.

Step3: Use angle - addition postulate

Since $\angle ABC=\angle ABD+\angle CBD$ and $m\angle ABC = 90^{\circ}$, by the angle - addition postulate, $m\angle ABD + m\angle CBD=90^{\circ}$. So C is "angle - addition postulate".

Step4: Simplify equation

Combining like terms in $m\angle CBD + m\angle CBD=90^{\circ}$ gives $2m\angle CBD = 90^{\circ}$. So D is $2m\angle CBD = 90^{\circ}$.

Answer:

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