Question

Select the correct answer from each drop-down menu. Given that zboc and zcod are complementary angles and bo intersects ad at point o, prove the following statements: 1. zboc and zcod are complementary angles. 2. m/boc = m/cod = 90��. 3. m/bod = 90��. 4. zaob and zbod are supplementary angles. 5. m/aob + m/bod = 180��. 6. mzaob = 90��. 7. m/aob = 90��. 8. m/aob = m/bod. 9. zaob ��� zbod. There is a missing step between true because of the 2. definition of complementary angles 3. substitution property of equality 5. definition of supplementary angles 6. substitution property of equality 7. subtraction property of equality 8. substitution property of equality 9. definition of congruent angles. Identify where in the proof there is a missing step and what this step should be.

Answer 1

1. True

2. True

3. True

4. False

5. True

6. False

7. False

8. True

9. True

Step-by-step explanation:

In the given geometric scenario, angles
`\(zboc\) and \(zcod\)` are complementary because they add up to
`\(90^\circ\)`, as per the definition of complementary angles. This is established by the angle relationships in the intersecting lines
`\(bo\) and \(ad\).` The missing step between true for statement 2 involves the application of the definition of complementary angles, affirming that
`\(m/boc\) and \(m/cod\) both equal \(90^\circ\).`

For statement 4,
`\(zaob\) and \(zbod\)` are not supplementary, contrary to the assertion. A missing step is the acknowledgment that complementary angles
`(\(zboc\) and \(zcod\))` do not necessarily imply supplementary angles between other pairs.

Regarding statement 6,
`\(mzaob\) is not necessarily \(90^\circ\)`, as the angles
`\(zaob\) and \(zboc\)` are not defined as complementary. Thus, the missing step here is the recognition that
`\(mzaob\)` is not constrained by the complementary angle definition.

Lastly, for statement 8, the missing step is the application of the substitution property of equality, showing that
`\(m/aob\)` is indeed equal to
`\(m/bod\)` within the context of the provided geometry. This establishes the equality relationship between these two angles.

In summary, the missing steps involve the careful application of angle definitions and properties to support the given statements within the geometric context.