Question

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

Answer 1

1. `mangle1 + mangle2 = 180^@`

Angles are said to be supplementary if they sum to `180^@`

2. Given

This is the second statement of the given information.

3. Definition of angle bisector

An angle bisector is a line, ray, or line segment that divides an angle into two equal parts. Depending on the teacher or work, it may also be prudent to add that `angle2` and `angle3` are the angles formed by the angle bisector `vec(BD)`

4. `mangle1+mangle3 = 180^@`

The substitution property of equality allows us to take two equal values and use them interchangeably in equations. In this case, we are substituting the equality in step 4 into the equation in step 2.

5. Definition of supplementary

See 1.