Angles and Parallel Lines - PowerPoint PPT Presentation

About This Presentation
Title:

Angles and Parallel Lines

Description:

Lesson 2-4 Angles and Parallel Lines * Lesson 2-4: Angles and Parallel Lines Lesson 2-4: Angles and Parallel Lines * Transversal Definition: A line that intersects ... – PowerPoint PPT presentation

Number of Views:290
Avg rating:3.0/5.0
Slides: 10
Provided by: kyus
Category:
Tags: angles | lines | parallel

less

Transcript and Presenter's Notes

Title: Angles and Parallel Lines


1
Lesson 2-4
  • Angles and Parallel Lines

2
Transversal
  • Definition A line that intersects two or more
    lines in a plane at different points is called a
    transversal.
  • When a transversal t intersects line n and m,
    eight angles of the following types are formed
  • Exterior angles
  • Interior angles
  • Consecutive interior angles
  • Alternative exterior angles
  • Alternative interior angles
  • Corresponding angles

t
m
n
3
Vertical Angles Linear Pair
  • Vertical Angles
  • Linear Pair

Two angles that are opposite angles. Vertical
angles are congruent.
? 1 ? ? 4, ? 2 ? ? 3, ? 5 ? ? 8, ? 6 ? ? 7
Supplementary angles that form a line (sum 180?)
?1 ?2 , ?2 ?4 , ?4 ?3, ?3 ?1, ?5 ?6,
?6 ?8, ?8 ?7, ?7 ?5
1
2
3
4
5
6
7
8
4
Angles and Parallel Lines
  • If two parallel lines are cut by a transversal,
    then the following pairs of angles are congruent.
  • Corresponding angles
  • Alternate interior angles
  • Alternate exterior angles
  • If two parallel lines are cut by a transversal,
    then the following pairs of angles are
    supplementary.
  • Consecutive interior angles
  • Consecutive exterior angles

Continued..
5
Corresponding Angles Consecutive Angles
  • Corresponding Angles Two angles that occupy
    corresponding positions.

? 2 ? ? 6, ? 1 ? ? 5, ? 3 ? ? 7, ? 4 ? ? 8
1
2
3
4
5
6
7
8
6
Consecutive Angles
  • Consecutive Interior Angles Two angles that lie
    between parallel lines on the same sides of the
    transversal.
  • Consecutive Exterior Angles Two angles that lie
    outside parallel lines on the same sides of the
    transversal.

m?3 m?5 180º, m?4 m?6 180º
1
2
m?1 m?7 180º, m?2 m?8 180º
3
4
5
6
7
8
7
Alternate Angles
  • Alternate Interior Angles Two angles that lie
    between parallel lines on opposite sides of the
    transversal (but not a linear pair).
  • Alternate Exterior Angles Two angles that lie
    outside parallel lines on opposite sides of the
    transversal.

? 3 ? ? 6, ? 4 ? ? 5
? 2 ? ? 7, ? 1 ? ? 8
1
2
3
4
5
6
7
8
8
Example If line AB is parallel to line CD and s
is parallel to t, find the measure of all the
angles when mlt 1 100. Justify your answers.
mlt280 mlt3100 mlt480
mlt5100 mlt680 mlt7100 mlt880
mlt9100 mlt1080 mlt11100 mlt1280
mlt13100 mlt1480 mlt15100 mlt1680
9
Example
If line AB is parallel to line CD and s is
parallel to t, find
1. the value of x, if mlt3 4x 6 and the mlt11
126.
2. the value of x, if mlt1 100 and mlt8 2x
10.
3. the value of y, if mlt11 3y 5 and mlt16
2y 20.
ANSWERS
1. 30
2. 35
3. 33
Write a Comment
User Comments (0)
About PowerShow.com