SOLUTION: Hello First of all in advance I thank you for the help you give me! Okay so here is the problem I am having a hard time with. Instruction: Write a paragraph proof for th

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Question 663230: Hello
First of all in advance I thank you for the help you give me!
Okay so here is the problem I am having a hard time with.
Instruction:
Write a paragraph proof for this form of Theorem 2-2.
If two angles are supplements of congruent angles, then the two angles are congruent.
Given: <1 and <2 are supplementary
<3 and <4 are supplementary
<2 is congruent to <4
Prove: <1 is congruent to <3
What I have:
By the definition of supplementary angles, m<1 + m<2=180 and m<1 + m<4=180. By substitution, m<1 + m<2= m<1 + m<4. Subtract m<1 from each side. You get m<2= m<4, or angle 2 is congruent to angle 4.
That is all I have so far...
However that would only prove...angle 2 is congruent to angle 4...it wouldn't prove what I need to prove...
May you help me?
Found 2 solutions by solver91311, MathLover1:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Defn Supplementary

Defn Supplementary

Defn Congruence

Transitive equality

Subtraction property of equality

Defn Congruent: Q.E.D.

John

My calculator said it, I believe it, that settles it

Answer by MathLover1(20855) (Show Source):
You can put this solution on YOUR website!
Proving Theorem 2-1
Given: < and < are supplementary
< and < are supplementary
< is congruent to <
Prove: < is congruent to <

Paragraph Proof:

By the Angle Addition Postulate, < +< = and < + < = .
By substitution, < +< = < + <.
It is given that < is congruent to <.
By substitution, < +< = < + <.
Subtract < from each side.
You get < = <, or < is congruent to <.