Difference between revisions of "Vertical Angle Theorem"
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The '''Vertical Angle Theorem''' is a [[theorem]] that states that all [[vertical angles]] are congruent. | The '''Vertical Angle Theorem''' is a [[theorem]] that states that all [[vertical angles]] are congruent. | ||
==Proof== | ==Proof== | ||
| − | Assume all angle measures to be in [[radians]]. A pair of vertical angles are formed by [[line|lines]] <math>\overline A \overline B</math> and <math>\overline C \overline D</math> and the intersection of these lines is P. Angles <math>\angle APC</math> and <math>\angle BPD</math> are vertical angles. Let <math>m\angle APC = x</math>. From this, <math>m\angle CPB = \pi-x</math>, so | + | Assume all angle measures to be in [[radians]]. A pair of vertical angles are formed by [[line|lines]] <math>\overline A \overline B</math> and <math>\overline C \overline D</math> and the intersection of these lines is P. Angles <math>\angle APC</math> and <math>\angle BPD</math> are vertical angles. Let <math>m \angle APC = x</math>. From this, <math>m\angle CPB = \pi-x</math>, so <math>m \angle BPD = \pi-(\pi-x)=x=m\angle APC.</math> |
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Revision as of 20:09, 4 September 2024
The Vertical Angle Theorem is a theorem that states that all vertical angles are congruent.
Proof
Assume all angle measures to be in radians. A pair of vertical angles are formed by lines 
and 
and the intersection of these lines is P. Angles 
and 
are vertical angles. Let 
. From this, 
, so 
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