| When two lines cross, 4 angles are formed. Let p be the point of intersection and move around p counterclockwise. Call the angles w x y and z. Note that x and y are supplementary, since they join to make one of the two lines. Similarly, y and z are supplementary, as they join to make the other line. Thus x+y = 180° and y+z = 180°. This means x = z. These are called vertical angles, on opposite sides of p. By the same reasoning, w and y are vertical angles, and are congruent. |
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When presented with vertical angles, one measurement determines everything. If w is 50° then so is y, while x and z are 130°. If w = 90° then all four angles are right angles. In this case the lines are said to be perpendicular.