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Arlecino [84]
3 years ago
9

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 ta

ble 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.

Mathematics
1 answer:
steposvetlana [31]3 years ago
7 0

Answer:

Step-by-step explanation:

by looking at the given image...

the shape ABCD is a parallelogram.

<u>Required:</u>

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°

<u><em>the  Statement  </em></u>  

1. ABCD is a parallelogram                

<em><u>the reason is..</u></em><em>    </em>

It is Given!

<u><em>the  Statement  </em></u>

2.m∠A=m∠C and m∠B=m∠D        

<em><u>the reason is..</u></em><em> </em>

Definition of parallelogram.

<u><em>the  Statement  </em></u>

3.m∠A+m∠B+m∠C+m∠D=360°    

<em><u>the reason is..</u></em><em> </em>

Definition of quadrilateral

<u><em>the  Statement  </em></u>

4. m∠A+m∠B+m∠A+m∠B=360°    

<em><u>the reason is..</u></em><em> </em>

By substitution

⇒ 2( m∠A + m∠B ) = 360°

⇒ m∠A + m∠B = 180°

it is also similar  m∠C + m∠D = 180°

<u><em>the  Statement  </em></u>

5.∠A and ∠C are supplementary

<em><u>the reason is..</u></em><em> </em>

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

Hope it helps!

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