Question

40 points 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: Prove: and are supplementary. and are supplementary. Answer: Statement Reason 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. 6. 6. 7. 7.

Answer 1

see below

Explanation:

by looking at the given image...

the shape ABCD is a parallelogram.

Required:

is to prove ∡A and ∡B are supplementary

and ∡C and ∡D are supplementary.

so, m∠A + m∠B = 180°

and m∠C + m∠D = 180°

the Statement

1. ABCD is a parallelogram

the reason is..

It is Given!

the Statement

2.m∠A=m∠C and m∠B=m∠D

the reason is..

Definition of parallelogram.

the Statement

3.m∠A+m∠B+m∠C+m∠D=360°

the reason is..

Definition of quadrilateral

the Statement

4. m∠A+m∠B+m∠A+m∠B=360°

the reason is..

By substitution

⇒ 2( m∠A + m∠B ) = 360°

⇒ m∠A + m∠B = 180°

it is also similar m∠C + m∠D = 180°

the Statement

5.∠A and ∠C are supplementary

the reason is..

by the definition of Supplementary ∠ B and ∠D are supplementary

Hope it helps!

Answer 2

Explanation:

by looking at the given image...

the shape ABCD is a parallelogram.

Required:

is to prove ∡A and ∡B are supplementary

and ∡C and ∡D are supplementary.

so, m∠A + m∠B = 180°

and m∠C + m∠D = 180°

the Statement

1. ABCD is a parallelogram

the reason is..

It is Given!

the Statement

2.m∠A=m∠C and m∠B=m∠D

the reason is..

Definition of parallelogram.

the Statement

3.m∠A+m∠B+m∠C+m∠D=360°

the reason is..

Definition of quadrilateral

the Statement

4. m∠A+m∠B+m∠A+m∠B=360°

the reason is..

By substitution

⇒ 2( m∠A + m∠B ) = 360°

⇒ m∠A + m∠B = 180°

it is also similar m∠C + m∠D = 180°

the Statement

5.∠A and ∠C are supplementary

the reason is..

by the definition of Supplementary ∠ B and ∠D are supplementary

Hope it helps!