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GMAT Lines and Angles

by ejkiv


July 19, 2015


GMAT Line (no different from regular lines): A geometrical object that is straight, infinitely long and infinitely thin.

GMAT Line

Segment: A line that has endpoints.

GMAT Lines and Angles

  Parallel: Two lines or segments that never meet - designated as // - AB // CD

GMAT Lines and Angles

Perpendicular: Two lines or segments the intersect to form a 90° angle. In drawings, this is represented with the drawing:  GMAT Perpendicular Lines.

GMAT Right Angle

Typically, these definitions will not be outright tested. Or, you will not see a question that asks you to define a parallel line, but that tidbit of information will be required for one step in solving the problem. Make sure you are comfortable with all of the wording so that you can quickly get to the important part: solving the problem.

Angle Facts    

Most often the line information above is used in combination with angles. Take the two segments below:

GMAT Supplementary Angles

The intersection of the line segments form supplementary angles.

Supplementary Angles: Two angles whose sum is 180° .

Whenever two lines or segments intersect they form supplementary angles. In this particular example this means that m° + n° = 180° . This will be used in many GMAT geometry problems.

Often times you will use this to set up equations or systems of equations. Take the following:

GMAT Opposite interior angles

If x + y = 50, then you can calculate n, which would equal 50°. This principle is called opposite interior angles. Basically, if you have a line segment that extends from the side of a triangle. The exterior angle n will be equal to the sum of the opposite interior angles x and y. This little fact can save you some time on the exam. However the key is that you can use the fact that the two angles created from line segment AB are supplementary and thus you can create the relationship of n and 180 - n. 

This also works with multiple line segments:

GMAT Lines and Angles

Side Note: Although this is probably not going to be tested, complementary angles are those that add up to 90° .

Let’s look at another example of intersecting lines to see how the idea of supplementary angles can help us gather more information about a diagram:

GMAT Vertical Angles

Looking at Diagram I you can come up with the following equations:

GMAT Angles equations

Also, a° = d° and the result is Diagram II. These are called vertical angles.

In addition to the examples above, you can gather more information if you have parallel lines. Take parallel lines AB and CD :

GMAT Vertical Angles

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