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The Fundamentals of Geometry Study Guide (page 3)

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Updated on Oct 5, 2011

Special Line Pairs

Parallel Lines

Parallel lines lie in the same plane and don't cross at any point:

The arrowheads on the lines indicate that they are parallel. The symbol is used to indicate that two lines are parallel: l m.

A transversal is a line that crosses two parallel lines. Line t is a transversal.

Introducing Geometry

When two parallel lines are crossed by a transversal, two groups of four angles each are formed. One group consists of ,, , and ; the other group contains , , , and .

The angles formed by the transversal crossing the parallel lines have special relationships:

  • The four obtuse angles are congruent:
  • The four acute angles are congruent:
  • The sum of any one acute angle and any one obtuse angle is 180°because the acute angles lie on the same line as the obtuse angles.
Hook: As a memory trick, draw two parallel lines and cross them with a transversal at a very slant angle. All you have to remember is that there will be exactly two sizes of angles. Since half the angles will be very small and the other half will be very large, it should be clear which ones are congruent. The placement of the congruent angles will be the same on every pair of parallel lines crossed by a transversal. Introducing Geometry

Perpendicular Lines

Perpendicular lines lie in the same plane and cross to form four right angles.

The little box where the lines cross indicates a right angle. Because vertical angles are equal, and the sum of all four angles is 360°, each of the four angles is a right angle. However, only one little box is needed to indicate this. Introducing Geometry
The symbol is used to indicate that two lines are perpendicular:
Don't be fooled into thinking two lines are perpendicular just because they look perpendicular. The problem must indicate the presence of a right angle (by stating that an angle measures 90°or by the little right angle box in a corresponding diagram), or you must be able to prove the presence of a 90°angle.

Tip

Look for acute, right, obtuse, and straight angles throughout the day. For instance, check out a bookcase. What is the size of the angle formed by the shelf and the side of the bookcase? Is it an acute, obtuse, or right angle? Imagine that you could bend the side of the bookcase with your bare hands. How many degrees would you have to bend it to create an acute angle? How about a straight angle? Take out a book and open it. Form the covers into an acute angle, a right angle, or a straight angle.

Find practice problems and solutions for these concepts at The Fundamentals of Geometry Practice Questions.

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