Transcript Holt Geometry 3-2

3-2
Angles Formed by Parallel Lines
and Transversals
Objective
Holt Geometry
10/29
Lesson 3.2
2
1
What is the name of the angle pair, angles 1 and 2?
3-2
Angles Formed by Parallel Lines
and Transversals
What if the lines are parallel?
2
1
Holt Geometry
3-2
Angles Formed by Parallel Lines
and Transversals
Postulate or
Theorem Name
What it says
Key Words
If 2 parallel lines are cut by a transversal, then…
Corresponding
…the corresponding
Angles
angles are congruent.
Postulate
Holt Geometry
Parallel lines
Transversal
Corresponding
angles
Picture
3-2
Angles Formed by Parallel Lines
and Transversals
Find mQRS.
Holt Geometry
3-2
Angles Formed by Parallel Lines
and Transversals
Example 1)
4
m
8
7
n
5
3
1
2
6
If m<8 = 61˚, find the measures
of all other numbered angles.
Holt Geometry
3-2
Angles Formed by Parallel Lines
and Transversals
Example 2)
4
m
8
7
n
5
3
1
2
6
Alternate Interior angles are ____________.
Alternate exterior angles are ____________.
Same-side interior angles are ____________.
Holt Geometry
3-2
Angles Formed by Parallel Lines
and Transversals
Alternate
…the alternate interior
Interior Angles
angles are congruent.
Theorem
Parallel lines
Transversal
Alternate interior angles
Alternate
…the alternate exterior
Exterior Angles
angles are congruent.
Theorem
Parallel lines
Transversal
Alternate exterior
angles
Same-side
Interior Angles
Theorem
Holt Geometry
Parallel lines
Transversal
…the same-side interior
Same-side interior
angles are supplementary. angles
Supplementary
3-2
Angles Formed by Parallel Lines
and Transversals
Find each angle measure.
A. mDCE
B. mCBG
Holt Geometry
3-2
Angles Formed by Parallel Lines
and Transversals
Example 3)
Given m3 = 3x-1
and m5 = x+5.
Find m1.
Holt Geometry
3-2
Angles Formed by Parallel Lines
and Transversals
Example 4)
Given m3 = 2(x-35)
and m4 = x+15.
Find m5.
Holt Geometry
3-2
Angles Formed by Parallel Lines
and Transversals
Objective
Holt Geometry
Exit Slip!
1. Let m1 = 120°, m2 = (60x)° .
a. Give the name of the angle pair that
describes <1 and <2.
b. Write and solve an equation to find the
measures of the angles.
c. Name the theorem or postulate that justifies your
solution.
2. Find m3 and m5 if m3 = (45x + 30)° and
m5 = (25x + 10)° .