Vertical Angles definition - Math Open Reference (original) (raw)

| | | Vertical Angles (also "opposite angles")From Latin: verticalis "overhead" Try this Drag an orange dot. Note the behavior of the vertical angles ∠JQM and ∠LQK. As can be seen from the figure above, when two lines intersect, four angles are formed. Each opposite pair are called vertical angles and are alwayscongruent. The red angles ∠JQM and ∠LQK are equal, as are the blue angles ∠JQL and ∠MQK. Vertical angles are also called opposite angles. Facts about vertical angles They are congruent Vertical angles are always congruent, or of equal measure. See ∠JQM and ∠LQK in the figure above. Adjust the lines and convince yourself of this fact. Sum of vertical angles Both pairs of vertical angles (four angles altogether) always sum to a full angle (360°). Adjacent angles In the figure above, an angle from each pair of vertical angles are adjacent angles and are supplementary (add to 180°). For example, in the figure above, m∠JQL + m∠LQK = 180°. In the figure above, adjust the lines and convince yourself of this fact. About the word 'vertical' 'Vertical' has come to mean 'upright', or the opposite of horizontal. But here, it has more to do with the word 'vertex'. Vertical angles are called that because they share a common vertex. Other angle topics General Angle definition Degrees Radians Angle bisector Subtended angle Interior of an angle Included angle Angle Types Acute angle Right angle Obtuse angles Straight angle Reflex angle Full angle Angle relationships Vertical angles Complementary angles Supplementary angles Linear pair Adjacent angles Corresponding angles Alternate interior angles Alternate exterior angles Interior angles of a transversal Exterior angles of a transversal (C) 2011 Copyright Math Open Reference. All rights reserved | | | - | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | |