3.1: Parallel Lines and Transversals

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3.1 Parallel Lines and Transversals

• Chapter 3 Angles and Triangles

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What is a Transversal?

• Lines in the same plant that do not intersect are
  called parallel lines.
• Lines that intersect at rights angles are called
  perpendicular lines.
• Transversal- a line that intersects two or more
  lines.
• When parallel lines are cut by a transversal,
  several pairs of congruent angles are formed.

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Corresponding Angles

• When a transversal intersects parallel lines,
  corresponding angles are congruent.

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Finding Angle Measures
Use the figure to find the measures of (a) lt1 and
(b) lt2.

• (a) lt1 and the 110 degree angles are
  corresponding angles. They are congruent
• So, the measure of lt1 is 110

• lt1 and lt2 are supplementary, The sum of the
  angles is 180 degrees.

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Practice
Use the figure to find the measure of lt1 and lt2.
explain your reasoning.

• lt1 and 63 degrees are corresponding angles, sot
  lt1 is 63 degrees.

• lt1 and lt2 are supplementary angles.

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Using Corresponding Angles
Use the figure to find the measures of the
numbered angles.

• lt1 and the 75 degree angle are vertical angles,
  so they are congruent.
• So, lt175

• The 75 degree angle is supplementary to both lt2
  and lt3.
• So, the measures of lt2 and lt3 are 105

Using corresponding angles, the measures of lt4
andlt6 are 75, and the measures of lt5 and lt7 are
105.
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Practice

• Use the figure to find the measure of the
  numbered angles.

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Interior and Exterior Angles

• When two parallel lines are cut by a transversal
• Four interior angles are formed on the inside of
  the parallel lines.
• Four exterior angles are formed on the outside of
  the parallel lines.
• lt3, lt4, lt5, and lt6 are interior angles.
• lt1, lt2, lt7, and lt8 are exterior angles.

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Using Corresponding Angles

• A store owner uses pieces of tape to paint a
  window advertisement. The letters are slanted at
  an 80 degree angle. What is the measure of lt1?

• Because all the letters are slanted at an 80
  degree angle, the dashed lines are parallel. The
  pieces of tape is the transversal.
• Using corresponding angles, the 80 degree angle
  is congruent to the angle that is supplementary
  to lt1.

The measure of lt1 is 180-80100 degrees.
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Alternate Interior and Alternate Exterior Angles

• When a transversal intersects parallel lines
• Alternate interior angles are congruent
• Alternate exterior angles are congruent

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Identifying Alternate Interior and Alternate
Exterior Angles
The photo shows a portion of an airport. Describe
the relationship between each pair of angles.

• lt3 and lt6 are alternate exterior angles.
• lt3 is congruent to lt6

• lt2 and lt7 are alternate interior angles.
• lt2 is congruent to lt7