Transcript 3.3 Parallel Lines and the Triangle Angle

Perpendicular Lines, Parallel
Lines and the Triangle AngleSum Theorem
Parallel Lines



Parallel lines are coplanar lines that do not intersect.
Arrows are used to indicate lines are parallel.
The symbol used for parallel lines is ||.
A
C
B
D
In the above figure, the arrows show that line AB is parallel to
line CD.
With symbols we denote, AB || CD .
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Theorem 3-7
If a||b
and b||c
Then a||c
It 2 lines are parallel to the same line, then they are parallel to
each other.
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PERPENDICULAR LINES
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

Perpendicular lines are lines that intersect to form a
right angle.
The symbol used for perpendicular lines is  .
4 right angles are formed.
m
In this figure line m is perpendicular to line n.
With symbols we denote, m  n
Lesson 2-3: Pairs of Lines
n
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Theorem 3-8
If m  t
and n  t
Then m || n
In a plane, if 2 lines are perpendicular to the same line, then
they are parallel to each other.
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3.3 Parallel Lines and the Triangle
Angle-Sum Theorem
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Theorem 3-10 Triangle Angle-Sum Theorem
The angles in a triangle add up to 180°
Triangle Angle-Sum Theorem
Find m<1.
1
35°
65°
Triangle Angle-Sum Theorem
ΔMNP is a right triangle. <M is a right angle and m<N
is 58°. Find m<P.
Using Algebra
G
Find the values of x, y, and z.
39°
65°
F
21°
x° y°
J
z°
H
Classifying Triangles
Equilateral: All sides congruent
Equiangular: All angles congruent
60°
60°
Acute Triangle: All angles are less than 90°
Right Triangle: One angle is 90°
Obtuse Triangle: One angle is greater than 90°
60°
Classifying Triangles
Isosceles: At least two sides congruent
Scalene: No sides congruent
Special Case
Equiangular Triangle = Equilateral Triangle
…and it’s also an Acute Triangle
60°
60°
60°
Classifying a Triangle
Classify the triangle by its sides and angles.
Classifying a Triangle
Classify the triangle by its sides and angles.
Using Exterior Angles of Triangles
Exterior Angle of a Polygon
1 Exterior Angle
m<1 = m<2 + m<3
2
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Remote Interior Angles
Theorem 3-11 Triangle Exterior Angle Theorem
The measure of the Exterior Angle is equal to the sum of the two
Remote Interior Angles
Using the Exterior Angle Theorem
Find the missing angle measure:
113°
40°
1
30°
70°
45°
45°
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2