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# Prove the second case of the congruent supplements theorem where two angles are...

iloveahobo | Student, Grade 10 | eNotes Newbie

Posted October 22, 2013 at 3:32 AM via web

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Prove the second case of the congruent supplements theorem where two angles are supplementary to congruent angles.

Given: <1 and <2 are supplements;
<3 and <4 are supplements;
<2 `~=`  <3

Prove:
<1  `~=` <4

Tagged with math, proving theorems

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted October 22, 2013 at 3:47 AM (Answer #1)

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It is given that `/_ 1` and` /_ 2` are supplementary.

`/_1 + /_2 = 180`

=> `/_2 = 180 - /_1`

Also, `/_3 + /_4 = 180`

=> `/_3 = 180 - /_4`

`/_ 2 ~= /_3`

=> `180 - /_1 ~= 180 - /_4`

=>` /_1 ~= /_4`

This shows that `/_1 ~= /_4`

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iloveahobo | Student , Grade 10 | eNotes Newbie

Posted October 22, 2013 at 3:50 AM (Reply #1)

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Thank you very much!

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