Transcript 3-4 Parallel Lines and the Triangle Angle

Parallel Lines and the Triangle Angle-Sum Theorem
LESSON 3-4
Additional Examples
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
HELP
AB.
ACB is a right angle.
Definition of right angle
Angle Addition Postulate
Subtract 70 from each side.
GEOMETRY
Parallel Lines and the Triangle Angle-Sum Theorem
LESSON 3-4
Additional Examples
Quick Check
(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
HELP
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.
GEOMETRY
Parallel Lines and the Triangle Angle-Sum Theorem
LESSON 3-4
Additional Examples
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.
Quick Check
HELP
GEOMETRY
Parallel Lines and the Triangle Angle-Sum Theorem
LESSON 3-4
Additional Examples
Find m1.
m1 + 90 = 125
m1 = 35
Exterior Angle Theorem
Subtract 90 from each side.
Quick Check
HELP
GEOMETRY
Parallel Lines and the Triangle Angle-Sum Theorem
LESSON 3-4
Additional Examples
Explain what happens to the angle formed by the back of the
chair and the armrest as you make a lounge chair recline more.
The exterior angle and the angle formed by the back of the chair and
the armrest are adjacent angles, which together form a straight angle.
As one measure increases, the other measure decreases.
The angle formed by the back of the chair and the armrest increases as
you lower the back of the lounge chair.
Quick Check
HELP
GEOMETRY