Download 3.5 Notes

Geometry
I've got a theory that
if you give 100
percent all of the
time, somehow
things will work out
in the end.
Larry Bird
Today:
•Homework Check
•3.5 Instruction
•Multiple Choice
Practice
•Practice
Yesterday
I've got a theory that
if you give 100
percent all of the
time, somehow
things will work out
in the end.
Larry Bird
•Recognize angle pairs that occur with parallel
lines.
• Prove that two lines are parallel from the
angle pairs.
Content Standards
G.CO.9 Prove theorems about lines and angles.
G.CO.12 Make formal geometric constructions with
a variety of tools and methods (compass and
straightedge, string, reflective devices, paper folding,
dynamic geometric software, etc.).
Mathematical Practices
1 Make sense of problems and persevere in solving
them.
3 Construct viable arguments and critique the
reasoning of others.
3.5 Proving Lines Parallel
Objectives:
1. Prove lines are parallel
Vocabulary:
parallel, transversal, corresponding,
alternate interior, alternate exterior,
consecutive interior
3.2 Review
If 2 parallel lines are cut by a transversal, then:
corresponding angles are congruent.
alternate interior angles are congruent.
alternate exterior angles are congruent.
consecutive interior angles are supplementary.
1 2
4 3
5 6
8 7
3.5 Proving Lines Parallel
The converse is also true:
If:
corresponding angles are congruent,
alternate interior angles are congruent,
alternate exterior angles are congruent,
consecutive interior angles are supplementary,
then the lines are parallel.
Determine which lines,
if any, are parallel.
Explain why!!!!
Answer:
Not b and c, because 77 + 100 is not 180 and
consecutive interior are supposed to be
supplementary.
Can move 77 with vertical, so 103 + 77 = 180.
Your Turn: Pair-Share
Determine which lines, if any, are parallel. EXPLAIN!
Answer:
Statements
Reasons
1. Given  ALWAYS
2. Vertical Angles Are Congruent.
3. Transitive Property of
Congruency.
4. Substitution Property of
Congruency.
5. If Alternate Interior Angles Are
Cong, Then Lines Are Parallel.
Which lines if any are parallel?
WHY?
l1
l2
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
l4
l3
Over Chapter 2
Name the property that justifies the statement.
If m1 + m2 = 75 and m2 = m3, then
m1 + m3 = 75.
A. Substitution Property
B. Reflexive Property
C. Addition Property
D. Symmetric Property
Over Chapter 2
If m1 = 9x + 6, m2 = 2(5x – 3),
and m3 = 5y + 14, find y.
A. y = 14
B. y = 20
C. y = 16
D. y = 24
Over Chapter 2
Find m1 and m2 if m1 = 8x + 18 and
m2 = 16x – 6 and m1 and m2 are
supplementary.
A. m1 = 106, m2 = 74
B. m1 = 74, m2 = 106
C. m1 = 56, m2 = 124
D. m1 = 14, m2 = 166
Over Lesson 3–4
containing the point (5, –2) in point-slope form?
A.
B.
C.
D.
Over Lesson 3–4
What equation represents a line with slope –3
containing the point (0, 2.5) in slope-intercept
form?
A. y = –3x + 2.5
B. y = –3x
C. y – 2.5 = –3x
D. y = –3(x + 2.5)
Over Lesson 3–4
containing the point (4, –6) in slope-intercept form?
A.
B.
C.
D.
Over Lesson 3–4
A.
B.
C.
D.
Geometry
I've got a theory that
if you give 100
percent all of the
time, somehow
things will work out
in the end.
Larry Bird
Assignment:
• 3.5 p 210 #6 9-15
odd, 17