GED Mathematical Reasoning: Introduction To Geometry

A line is a straight path made up of points. When we draw a line, we use arrows on each end to denote that a line extends in both directions forever.

  • A horizontal line runs left to right.  To remember the definition of a horizontal line, think of the horizon of a landscape. A horizontal line runs left to right, just like the horizon.
  • Parallel lines are side by side. They are the same distance from each other at every point. Parallel lines never touch each other or cross paths. When you think of parallel lines, you might think of the rails on a railroad track or the double yellow line in the center of the road.

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  • Perpendicular lines cross each other at a corner angle. You might think of a four way stop on the roadway as a “real world” example of perpendicular lines.

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The symbol we use to denote an angle looks like an angle \angle. We measure the size of angles in degrees, which we denote using the symbol shown here on the slide: \circ.

  • It is common to think of angle measure in terms of a circle. A circle contains 360 degrees.

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  • So 1^{\circ} is \frac{1}{360} of a circle.

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  • 45^{\circ} is \frac{45}{360} of a circle, which reduces to one-eighth of a circle.

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  • And 90^{\circ} is \frac{90}{360} of a circle, which reduces to one-fourth of a circle.

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Examples of each type of angle are shown here. Notice that we use a small square to denote the 90 degree angle of the right angle.

Four classifications of angles according to size:

  • Acute angle – greater than zero degrees, but less than 90 degrees
  • Right angle – exactly 90 degrees
  • Obtuse angle – greater than 90 degrees but less than 180 degrees
  • Straight angle – exactly 180 degreesmeas23

 

Example 1

Use the diagram to answer the following questions.

  1. What line is vertical?
  2. What line is horizontal?
  3. What lines are parallel to each other?
  4. What lines are perpendicular to each other?

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Notice that the diagram pictured with Example 1 is composed for FOUR lines.

A vertical line runs up and down. To answer part (1) of Example 1, line A is a vertical line.

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A horizontal line runs left to right. To answer part (2) of the example, line D is a horizontal line. A horizontal line runs left to right, just like the horizon.

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Parallel lines are side by side. They are the same distance from each other at every point. Parallel lines never touch each other or cross paths. So to answer part (3) of Example 1, lines B and C are parallel.

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Now let’s talk about perpendicular lines. Perpendicular lines cross each other at a corner angle. For part (4) of the example, lines A and D are perpendicular to each other.

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Example 2

A waiter is cutting a circular pizza into 8 equal slices. At what angle should he cut the sides of each piece?

 

In Example 2, the waiter would like to cut a circular pizza into 8 equal slices. In other words, he would like to divide 360 degrees into 8 equal angles. To do this, we need to divide 360 by 8. Whether we compute this by hand or using a calculator, the answer is: 45. Therefore, the waiter should cut the sides of each piece at 45 degree angles.meas22

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