Vertical Angles
created by an X; congruent; points touch
Vertical angles are a pair of angles formed by two intersecting lines. Specifically, when two lines intersect, they form four angles, of which two are vertical angles. The two vertical angles are opposite each other and have equal measures.
For example, in the image below, angle A and angle C are vertical angles, as are angle B and angle D. The measure of angle A is equal to the measure of angle C, and the measure of angle B is equal to the measure of angle D.
“`
A
|\
| \
| \
——|—\——
| \
| \
| \
C B
“`
Vertical angles have several properties that are useful in geometrical reasoning. For instance, if the measure of one vertical angle is known, the measure of the opposite vertical angle can be found since they are congruent. Additionally, if two lines are known to be parallel, then the corresponding vertical angles are congruent.
It is also worth noting that vertical angles always have opposite orientation. For example, if angle A is measured clockwise, then angle C will be measured counterclockwise.
More Answers:
Understand Linear Pairs, Same Side Interior, And Same Side Exterior Angles In MathMastering Geometry: Vertical, Corresponding, Alternate Interior, And Alternate Exterior Angles
Complementary Angles: Exploring The Relationship Between Angles In Geometry.