Question

1. 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: Angle A and B are supplementary. C and d are supplementary.

Answer 1

Given: ABCD is a parallelogram.

Prove: Angle A and B are supplementary and C and D are supplementary.

That is, m∠A + m∠B = 180° and m∠C + m∠D = 180°

Statement Reason

1. ABCD is a parallelogram 1. Given

2.m∠A=m∠C and m∠B=m∠D 2. Definition of parallelogram.

3.m∠A+m∠B+m∠C+m∠D=360° 3. Definition of quadrilateral

4. m∠A+m∠B+m∠A+m∠B=360° 4. By substitution

⇒ 2( m∠A + m∠B ) = 360°

⇒ m∠A + m∠B = 180°

Similarly, m∠C + m∠D = 180°

5.∠A and ∠C are supplementary, 5. Def. of Supplementary

∠ B and ∠D are supplementary