Question

A conjecture and the two-column proof used to prove the conjecture are shown. Match each expression or phrase to the appropriate statement or reason?

Answer 1

1) Given

This is our initial premise.

2) Linear pairs of angles are supplementary

This one is a little questionable, as some definitions of linear pairs require supplementary angles, whereas others only require the intersection of two lines. Check your book or notes for any given theorems regarding supplementary angles.

3) `mangleABC + mangleCBD = 180^@`

The definition of supplementary angles is that two angles are supplementary if their measures sum to `180^@`.

4) Substitution of 1. into 3.

As with 2), this may differ based on the teacher or book. Some may prefer that you write out the equation, whereas others may be satisfied with the references as given. Check for similar examples.

5) `mangleABC = 90^@`

Subtracting `90^@` from each side of 4. gives us the above result.

6) Definition of right angle

By definition, a right angle is one whose measure is `90^@`.