Question

writing a two-column proof

statements | reasons

1. ∠abc is rt. ∠ | 1. a
2. db bisects ∠abc | 2. given
3. b | 3. def.of rt. ∠
4. m∠abd = m∠cbd | 4. def. of bis.
5. m∠abd + m∠cbd = 90° | 5. c
6. m∠cbd + m∠cbd = 90° | 6. subs. prop.
7. d | 7. add
8. m∠cbd = 45° | 8. div. prop.

identify the missing parts in the proof.
given: ∠abc is a right angle.
db bisects ∠abc.
prove: m∠cbd = 45°
a: dropdown with given
b: dropdown with measure of angle abc = 90
c: dropdown with angle addition postulate
d: dropdown with options: angle abc = 90, angle abd = 90, 2 times the measure of angle abc = 90, 2 times the measure of angle cbd = 90

Explanation:

Step1: Analyze D's context

From step 6: \( m\angle CBD + m\angle CBD = 90^\circ \), which is \( 2m\angle CBD = 90^\circ \). So D should be \( 2 \times m\angle CBD = 90^\circ \).

Step2: Confirm the logic

Since \( m\angle ABD = m\angle CBD \) (step 4) and \( m\angle ABD + m\angle CBD = 90^\circ \) (step 5), substituting gives \( 2m\angle CBD = 90^\circ \), so D is \( 2 \) times the measure of angle \( CBD = 90^\circ \).

Answer:

2 times the measure of angle CBD = 90