Transcript 3-5 Parallel Lines and Triangles

Bellringer
Find the slope going through
the points.
 1.
 2. (2, 3), (1, 6)
 1. m=-2/3
 2.m=3
Use the given information to
write an equation for each line.
 3. slope 1/3 , y-intercept
2
 4.
 3. y=-1/3x-2
 4.y=-3/2x+2
Geometry: Chapter 3 Parallel and
Perpendicular lines
3-5 PARALLEL LINES AND
TRIANGLES
Connections
Lesson Purpose
Objective
Essential Question
 To use parallel lines to
 How do the postulates and
prove a theorem about
triangles.
 To find measures of angles
of triangles.
theorem for proving
triangles congruent
shorten the time and work
involved?
Postulate 3-3 Parallel
Postulate
 Through any point not on a line, there is one
and only one line parallel to the given line.
 There is exactly one line through Parallel to
m.
P
•
m
Triangle Angle-Sum Theorem 3-10
 The sum of the measures of the angle of a
triangle is 180.
Example #1
(1) Find the measure of ∠C.
 So we have

. Using the diagram, we are
given that
mA= 120
mB=34
 A+B+C=180
Using the angle
measures we were given,
we can substitute those
values into our equation
to get.


120+34+mC=180
mC=26
Example #2
 (2) Find the value of x
in the diagram below.
 mS+mT+mSRT=180
 61+73+mSRT=180
 mSRT= 46
 SRTQRP thus,
 QRP=46
 P+Q+46=180
 x+x+46=180
 mS=61
 2x+46=180
 mT=73
 P=Q=67
 mP=mQ=x
Key Concepts
 The angle formed by one side of
a triangle with the extension of
another side is called an
exterior angle of the triangle.
Key Concepts
 Exterior angles get their name because they lie on the
outsides of triangles.
 The two angles that are not adjacent, or next to,
the exterior angle of the triangle are called remote
interior angles.
Triangle Exterior Angle
Theorem 3-11
 The Measure of each
exterior angle of a
triangle equals the sum
of the measures of its
two remote interior
angles.
Example #3
1) Find the measures of ∠1
and ∠2 in the figure below.
Solution
 mS=42, and mA=30
 mS+mA+1=180
 42+30+1=180
 72+1=180
 1=108
 mS+mA= 2
 42+30=2
 2=72
Example #4
2) Find m∠B.
Solution
 R=93, and JEB=132
 B=9x+3
 R+B=JEB
 93+(9x+3)= 132
 96+9x=132
 9x=36
 x=4
 B=39
Real World Connections
Summary-Recap
 The sum of the measures of the angles of a
triangle is equal to 180.
 The measure of each exterior angle of a
triangle equals the sum of the measures of its
two remote interior angles.
Ticket Out and Homework
Ticket Out
 What is true about the
measures of angles in a
triangle?
 By the Triangle Angle Sum
theorem, The sum of the
measures of the angles of a
triangle are equal to 180
Homework
 pg.184-185 #s
10,14,20,24,25