Vertical (angles)

From Wikipedia, the free encyclopedia

Two lines intersect to create two(2) pairs of vertical angles. One pair consists of angles A and B; the second pair consists of angles C and D.

A pair of angles is said to be vertical (US English) or vertically opposite (British English) if the angles share the same vertex and are bounded by the same pair of lines but are opposite to each other. Such angles are congruent and thus have equal measure.^[1]

[edit] Vertical Angle Theorem

If two line segments, EF and GH, intersect at the point P, they form four angles, EPG, GPF, FPH, and HPE. These angles can be grouped into two pairs of vertical angles: one vertical pair contains EPG and FPH, and the other pair contains GPF and HPE. Any angle in the first pair is supplementary to any angle in the second pair.^[2] The most obvious way to tell if two angles are vertical angles are if they form an "X". A vertical angle is an angle that intersects with another one.

[edit] Proof of the Vertical Angle Theorem

This theorem can be proved in an algebraic way. Assume that angle A in the picture is equal to the measure x, and then subtract x from 180 (the amount of degrees in a line) to get angle C, or 180-x. Then, to find angle B, subtract the quantity "180-x" from 180. This means that angle B is equal to 180-(180-x), or 180-180+x, which equals x. Finally, angle D can be found algebraically by subtracting angle B from 180, which equals 180-x. Angles A and B are both equal to x, so angles A and B are equal. As well, angles C and D are both equal to 180-x, so angles C and D are equal.

[edit] External links

• Definition and properties of vertical angles With interactive applet
• Angle definition pages with interactive applets that are also useful in a classroom setting. Math Open Reference

[edit] References

This geometry-related article is a stub. You can help Wikipedia by expanding it.