Question

statements

1. ( mangle aob

eq mangle cod )

1. ( mangle aob + mangle boc

eq mangle boc + mangle cod )

1. ( mangle aoc

eq mangle bod )

1. ( mangle aoc = mangle bod )
2. ( mangle aob = mangle cod )

reasons

1. assumption
2. addition property of equality
3. angle addition postulate
4. given
5. by contradiction

ken wrote a direct proof using deductive evidence
betty wrote an indirect proof using deductive evidence
betty wrote a direct proof using contradiction.
ken wrote a direct proof using contradiction.
ken wrote an indirect proof using deductive evidence
betty wrote an indirect proof using contradiction.

Explanation:

An indirect proof (proof by contradiction) starts with an assumption that is the opposite of what is to be proved. Here, the proof starts with the assumption \(m\angle AOB
eq m\angle COD\) (step 1). Then, through a series of logical steps (using addition property of equality, angle - addition postulate, and given information), a contradiction (\(m\angle AOC
eq m\angle BOD\) contradicts \(m\angle AOC = m\angle BOD\)) is reached. Deductive evidence is used as each step follows from a known property, postulate, or given.

Answer:

Betty wrote an indirect proof using deductive evidence.