Download Chapter 3: Parallel Lines and the Triangle Angle

Warm Ups
Classify each angle
1.
2.

3.
Solve Each Equation
4. 30+90+x=180
5. 55+x+105=180
6. x + 58 = 90
7. 32 + x = 90
Chapter 3:
Parallel Lines and the Triangle
Angle-Sum Theorem
Properties of parallel and
perpendicular lines.
 Prove that lines are parallel.

Triangle Angle-Sum Theorem

The sum of the measure of the angles of a
triangle is 180.
mA  mB  mC  180
A
C
B
Triangle Angle-Sum Theorem
“The sum of the measures of the
angles of a triangle is 180. “

Ex: A triangle has m<1=35 degrees and
m<2=65 degrees. Find m<3.

Ex: Triangle MNP is a right triangle. <M is
the right angle and m<N is 58. Find m<P.
Parallel Lines and the Triangle
Angle-Sum Theorem
Find m
Z.
48 + 67 + m
Z = 180
Triangle Angle-Sum Theorem
115 + m
Z = 180
Simplify.
Z = 65
Subtract 115 from each side.
m
Parallel Lines and the Triangle AngleSum Theorem
In triangle ABC,
ACB is a right angle, and CD
Find the values of a, b, and c.
Find c first, using the fact that
m
ACB = 90
c + 70 = 90
c = 20
ACB is a right angle.
Definition of right angle
Angle Addition Postulate
Subtract 70 from each side.
AB.
Parallel Lines and the Triangle Angle-Sum Theorem
(continued)
To find a, use
ADC.
a+m
ADC + c = 180
m ADC = 90
a + 90 + 20 = 180
a + 110 = 180
a = 70
To find b, use CDB.
70 + m CDB + b = 180
m
CDB = 90
70 + 90 + b = 180
160 + b = 180
b = 20
Triangle Angle-Sum Theorem
Definition of perpendicular lines
Substitute 90 for m ADC and 20 for c.
Simplify.
Subtract 110 from each side.
Triangle Angle-Sum Theorem
Definition of perpendicular lines
Substitute 90 for m
CDB.
Simplify.
Subtract 160 from each side.
Triangles
Equiangular – all angles congruent
Acute – all angles acute
Right – one right angle
Obtuse – one obtuse angle
Equilateral – all sides congruent
Isosceles – at least two sides congruent
Scalene – no sides congruent
Parallel Lines and the Triangle AngleSum Theorem
Classify the triangle by its sides and its angles.
The three sides of the triangle have three different lengths,
so the triangle is scalene.
One angle has a measure greater than 90, so the triangle is obtuse.
The triangle is an obtuse scalene triangle.
More Triangles
Exterior Angle of a polygon is an angle
formed by a side and an extension of an
adjacent side.
 Remote Interior Angles are the two
nonadjacent interior angles for each
exterior angle

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
2
1
3
Parallel Lines and the Triangle Angle-Sum Thm
Find m
m
1.
1 + 90 = 125
Exterior Angle Theorem
m
Subtract 90 from each side.
1 = 35
HOMEWORK
Page
134
2-36 Evens
44-47