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I'm doing some Geometry work and I'm wondering how you would prove that two angles are congruent. I know that they are of the same angle size but I'm not sure why or how to prove it exactly.

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Angles Or Triangles? –  Inceptio Apr 13 '13 at 15:01
    
Yes congruent, vertical angles theorem, can you make it simple please and explain... –  user61406 Apr 13 '13 at 15:02
    
Sometimes what you are talking about can be problem specific. Can you give us the problem? –  mtiano Apr 13 '13 at 15:05
    
Normally people say angles are "equal", not congruent. –  Stefan Smith Apr 13 '13 at 15:10
    
@StefanSmith: Normally, figures (segments, angles, triangles) are "congruent"; numbers (lengths, measures, areas) are "equal". –  Blue Apr 13 '13 at 15:19
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2 Answers

I'm not sure what exactly you're looking for. Since, you have mentioned about Vertical Angle theorem, here it is. When two lines intersect at a point. The vertically opposite angle are equal.

Vertically opposite angles

In this case, you see $\angle CXB= \angle AXD$ eventually other pair is equal.

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Oh ok thanks a lot –  user61406 Apr 13 '13 at 15:16
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enter image description here

Oh right, Angle 1 is congruent to angle 3 because they are verticle angles right?

1 + 2 = 180

2 + 3 = 180

1 + 2 = 2 + 3

1 = 3

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1+3=180 is wrong, either 1+2=180 or 1+4 =180. You're proof is right if you rename two of the angles, I guess it was just a little confusion. –  MyUserIsThis Apr 13 '13 at 15:28
    
It seems you didn't consider everything again when you edited your answer. I changed it for you ^_^ EDIT: Until someone reviews it at least... –  Jerry Apr 13 '13 at 17:18
    
oh ok thanks jerry! –  user61406 Apr 14 '13 at 10:28
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