Geometry Chapter 2: Intersecting Angles

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When two lines intersect each other, they create four angles:

In this case, the angles opposite one another are called vertical angles. As you can see, vertical angles are by definition always equal to each other. Therefore, in this case, 1 = 2, and 3 = 4.

Parallel Lines

Two lines that never intersect and never get closer or farther away from one another are called parallel lines. || is the symbol for parallel lines. In the following figure, a || b, or line a is parallel to line b:

Vertical Angles

When two parallel lines are cut by a third line, they form a system of vertical angles.

In this figure, we can see that 1 and 4 are equal, as are 5 and 8. But because they are formed by two parallel lines, they are all equal to each other. The same could be said for angles 2, 3, 6, and 7. There are many terms from geometry class you may know to describe these angles, such as “alternate interior” or “alternate exterior,” but these terms are not used on the test. For the GMAT, it is simply enough to know that all the little angles will always be equal, and all the big angles will always be equal. Additionally, you should realize that any little angle added to any big angle will always equal 180°.

Perpendicular Lines

When two lines intersect each other at a 90° angle, they are said to be perpendicular to one another. is the symbol for perpendicular, and mn means that m is perpendicular to line n.

Midpoint and Bisect

Two more vocabulary words you need before you can finish this section.

Midpoint is the center point of any line. In the example below, point b is the midpoint of line ac.

Bisect means “to cut in half”. Anything can be bisected: a line, an angle, a circle, a square. In the figure above, point b “bisects” line ac.

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Contents of Geometry Chapter: Table of Contents Chapter 1: Angles and Lines   Chapter 2: Intersecting Angles   Chapter 3: Triangles   Chapter 4: Circles   Chapter 5: Perimeters & Areas   Chapter 6: Solids   Chapter 7: Coordinate Geometry    Chapter 3: Triangles

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