SOLUTION: Given: Angle 1 is congruent to angle 3. Prove: Angle 2 is congruent to angle 4. *Angle 1 and 2 are vertical angles. Angle 3 and 4 are vertical angles.

Algebra ->  Geometry-proofs -> SOLUTION: Given: Angle 1 is congruent to angle 3. Prove: Angle 2 is congruent to angle 4. *Angle 1 and 2 are vertical angles. Angle 3 and 4 are vertical angles.      Log On


   

Question 624775: Given:
Angle 1 is congruent to angle 3.
Prove:
Angle 2 is congruent to angle 4.
*Angle 1 and 2 are vertical angles.
Angle 3 and 4 are vertical angles.
Found 2 solutions by jim_thompson5910, Alan3354:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Angles 1 and 2 are vertical angles. So angle 1 = angle 2 because vertical angles are congruent.

Angles 3 and 4 are vertical as well. So angle 3 = angle 4 by the same reason.

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Since it's given that "Angle 1 is congruent to angle 3. ", this also means that angle 1 = angle 3

Now we can use substitution to get

angle 1 = angle 3


angle 2 = angle 3 << -- replace "angle 1" with "angle 2" (since the two are congruent)

angle 2 = angle 4 << -- replace "angle 3" with "angle 4" (since the two are congruent)

So because we've shown that angle 2 = angle 4 , this proves Angle 2 is congruent to angle 4

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
Angle 1 is congruent to angle 3.
Prove:
Angle 2 is congruent to angle 4.
*Angle 1 and 2 are vertical angles.
Angle 3 and 4 are vertical angles.
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An angle is measured between 2 lines, there is no "vertical angle."
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Post a sketch so we'll know what you mean.