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3.1: Parallel Lines and Transversals

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3.1: Parallel Lines and Transversals Chapter 3: Angles and Triangles What is a Transversal? Lines in the same plant that do not intersect are called parallel lines. – PowerPoint PPT presentation

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Title: 3.1: Parallel Lines and Transversals


1
3.1 Parallel Lines and Transversals
  • Chapter 3 Angles and Triangles

2
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.

3
Corresponding Angles
  • When a transversal intersects parallel lines,
    corresponding angles are congruent.

4
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.

5
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.

6
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.
7
Practice
  • Use the figure to find the measure of the
    numbered angles.

8
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.

9
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.
10
Alternate Interior and Alternate Exterior Angles
  • When a transversal intersects parallel lines
  • Alternate interior angles are congruent
  • Alternate exterior angles are congruent

11
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
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