Write a two-column proof for the following conjecture. You may not need to use all of the rows of the twocolumn table provided below. You may also add additional rows if needed.

Question

I need help asap or I might fail my semester!

Write a two-column proof for the following conjecture. You may not need to use all of the rows of the two column table provided below. You may also add additional rows if needed.

Given: Parallelogram ABCD

Prove: ∠A and ∠B are supplementary.

∠B and ∠C are supplementary

Answer 1

Again, this proof would be much easier if I could draw the parallelogram in question. But I will try to describe it in writing.; Draw the following parallelogram with line segments AB and CD drawn horizontally with CD below AD and points A and C on the left hand side Now complete your parallelogram with line segments AB and DC parallel to one another with AB to the left of DC and points D and C on the top. Finally extend two dotted lines: one to the left of B and label that angle as B*; the other line to the right of point D and label that angle D^* . Now we can perform our two column proof:

Statement Reason

AB is parallel to DC & AD is parallel to BC Definition of a Parallelogram

Angle A is congruent to Angle B^* Alternate interior angles are congruent

BC is a straight angle Definition of a straight angle

Measure angle B + angle B^* = 180 degrees Measure of straight angle = 180 degrees

Angle A is supplementary to Angle B Definition of supplementary angles

Similarly

Angle C is congruent to Angle D* Alternate interior angles are congruent

CD is a straight angle Definition of a straight angle

Measure angle D + angle D^* = 180 degrees Measure of straight angle = 180 degrees

Angle B is supplementary to angle C Definition of supplementary angles

Answer 2

Statements Reasons

1.Parallelogram ABCD 1. Given

2.∠A and ∠B are supplementary 2. Theorem that says consecu-

∠B and ∠C are supplementary tive angles of a parallelogram

are supplementary.