Download 3.3 Relating Parallel and Perpendicular Lines  a Theorem 3-9:

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Transcript
3.3 Relating Parallel and Perpendicular Lines
a
b
c
Theorem 3-9: If two lines are parallel to the same line, then
they are parallel to each other.
a || b

Relating Parallel and Perpendicular Lines
t
m
n
Theorem 3-10: In a plane, if two lines are perpendicular to the
same line, then they are parallel to each other.
m || n

Relating Parallel and Perpendicular Lines
t
m
1
2
n
Given : m  t, n  t
Prove : m || n
Statements
Reasons
1. m  t, n  t
1.
2. 1 and 2 are
right angles
2.
3. 1  2
3.
m || n
4.
4.
Relating Parallel and Perpendicular Lines
n
l
m
Theorem 3-11: In a plane, if a line is perpendicular to one of
two parallel lines, then it is also perpendicular to the other.
nm

Relating Parallel and Perpendicular Lines
n
1
l
2
Given : n  l, and l || m
Prove : n  m
Statements
Reasons
1. n  l, and l || m
1.
2. 1 is a right 
2.
3.
3. Corresp.  ‘s post.
4. n  m
4.
m
3.4 - Finding Angle Measures in Triangles
C
50°
35°
A
B
Theorem 3-12: Triangle Angle-Sum Theorem:
The sum of the measures of the angles of a triangle is 180.
mA  mB  mC  180

Finding Angle Measures in Triangles
Finding Angle Measures in Triangles
G
Find the values of x, y, and z.
39°
21°
65° x° y° z°
F
J
H
Finding Angle Measures in Triangles
B
Find the values of x, y, and z.
x°y°
z° 49°
62°
A
C
D
Classifications of Triangles
Equiangular
All 's are 
Acute
All 's acute

Equilateral
All sides 
Right
One right 
Obtuse
One obtuse 


Isosceles
At least 2 sides 
Scalene
No sides 
Classifications of Triangles
Classify the following triangles by their angles and sides.
37°
37°
Using Exterior Angles of Triangles
Exterior Angle of a Polygon: An angle formed by a side and an
extension of an adjacent side.
Exterior
Angle
2
1
3
Remote
Interior
Angles
Remote Interior Angles: The two nonadjacent interior angles
corresponding to each exterior angle of a triangle.
Using Exterior Angles of Triangles
100°
x°
50°
Using Exterior Angles of Triangles
2
1
3
Theorem 3-13: Triangle Exterior Angle Theorem:
The measure of each exterior angle of a triangle equals the sum
of the measures of its two remote interior angles.
m1  m2  m3

Using Exterior Angles of Triangles
Find the values of w, x, y, and z.
x°
97°
y°
53°
w°86° z°
Little Mo’ Practice
Find the value of x.
(80 – 2x)°
(70 – 3x)°
Homework #14
 3.3 Proof Worksheet
 Pg 150 #1-6, 18-20, 23-26
 3.1-3.4 QUIZ MONDAY!!!!!!