Download Section:

Section: 3-1
Name:
Topic: Properties of
Class: Geometry 1A
Parallel Lines
Period:
Standard: 1
Date:
Transversal
 A transversal is a line that intersects two coplanar lines at two
distinct points.
2
3
1
4
5
8
7
6
How many angles are
formed? There are _____ angles.
______________________________________________________
Exterior Angles The exterior angles are ________________________________.
Interior Angles The interior angles are ________________________________.
Alternate Interior Angles  ____ and  _____ are alternate interior angles. Name another
Alternate means
______________
pair of alternate interior angles.  ____ and  _____
Alternate Exterior Angles  ____ and  _____ are alternate exterior angles. Name another
pair of alternate exterior angles.  ____ and  _____
Corresponding Angles
 ____ and  _____ are corresponding angles. Name three more
pairs of corresponding angles.  ____ and  _____
 ____ and  _____
Same-Side Interior
Angles
 ____ and  _____
 ____ and  _____ are same-side interior angles. Name another
pair of same-side interior angles.  ____ and  _____
1
What happens to the
angles when the lines are
parallel?
1. Draw any non-perpendicular transversal.
2. Label two corresponding angles as 1 and 2.
3. Use patty paper to measure the opening of 1.
How does the measure of 1 compare to the measure of 2?
Corresponding Angles
The corresponding angles formed by parallel lines and a
transversal are ___________________________.
m
n
m n
Alternate Interior Angles
1. Draw any non-perpendicular transversal.
2. Label two alternate interior angles as 3 and 4.
3. Use patty paper to measure the opening of 3.
How does the measure of 3 compare to the measure of 4?
The alternate interior angles formed by parallel lines and a
transversal are ___________________________.
m
m n
n
2
Alternate Exterior Angles
1. Draw any non-perpendicular transversal.
2. Label two alternate exterior angles as 5 and 6.
3. Use patty paper to measure the opening of 5.
How does the measure of 5 compare to the measure of 6?
The alternate exterior angles formed by parallel lines and a
transversal are ___________________________.
m
n
m n
What about same-side
interior angles? Are they
congruent too?
m
8
7
9
m n
n
We know that 7  _____ and 7 + _____ = 180.
By substitution  _____ +  _____ = 180.
Therefore same-side angles formed by parallel lines are
_______________________________.
Summary/Reflection: The letters Z, F and C can be used to help you identify types of angles.
Name the type of angle illustrated by each letter.
3
Section: 3-2
Name:
Topic: Proving Lines
Class: Geometry 1A
Parallel
Period:
Standard:
Date:
How do we know a b ?
How can we PROVE a b ?
b
150
10x
2x
a
 To PROVE two lines are parallel we must use information we
KNOW to be true.
Use this fact to
determine x and then
substitute back into the
diagram.
What is true about the diagram above?
_____________________________________
To PROVE two lines are parallel you can use one of the following.
 If _________________________ angles are congruent, then
the lines are parallel.
 If _________________________ angles are congruent, then
the lines are parallel.
 If _________________________ angles are supplementary,
then the lines are parallel.
Summary/Reflection: In the diagram below, what does x have to be for r s ?
45
(2x-5)
s
r
4
Section: 3-3
Name:
Topic: Triangles, Parallel
Class: Geometry 1A
Lines & the Triangle Angle-
Period:
Sum Theorem
Date:
Standard:
Types of Triangles
Classify by Angles
Classify by Sides
Sum of the Interior Angles
of a Triangle
ACUTE
RIGHT
OBTUSE
EQUILATERAL
ISOSCELES
SCALENE
1.
2.
3.
4.
5.
Trace the triangle you were given in the space below.
Identify the triangle (by sides and angles).
Label the angles as 1, 2 and 3.
Tear off the angles and label the empty spaces as 1, 2 and 3.
Line up vertices of the three angles and make them share sides.
What is the sum of the interior angles of a triangle? __________
5
Triangle Angle-Sum
Theorem
Examples
All the angles in a triangle add up to ____________.
1.
3x
2x
x
2.
y
20
Exterior Angles of a
Triangle
What do we know about the triangle below? What else can we
conclude?
4
1
2
3
The ___________________ angle equals the sum of the
____________________ interior angles.
6
Examples 1. What is the value of x?
x
52
115
2. ABC is isosceles with AB the base. AC = 3x, AB = 10 and
BC = 45. What is the value of x?
C
A
B
Summary/Reflection: Draw each triangle below or tell why it is impossible to draw.
A. Isosceles right triangle
B. Scalene obtuse triangle
C. Right obtuse triangle
D. Equilateral right triangle
7
Section:
5-5
Topic: Inequalities in
Triangles
Standard:
6
Name:
Class: Geometry 1A
Period:
Date:
Triangle Inequality
Theorem
The __________________ of the lengths of any 2 sides
of a triangle is __________________________ the
length of the third line.
a + b > ________
b + c > ________
a + c > ________
a
Example 1
b
c
Will a 3 inch, 6 inch, and 8 inch sticks form a triangle?
Check conditions: 3 + 6 ______ 8
6 + 8 ______3
3 + 8 ______6
Example 2 What size stick could you use to create a triangle with 2
inch and 7 inch sticks?
Any stick _________________ _________________
and ________________ inches.
In symbols _____________________.
8
One Triangle Inequality
Theorem
Use a ruler to draw an obtuse scalene triangle in the space below.
Then use a ruler and protractor to determine the side lengths and
angle measures.

The longest side is across from the
___________________ angle.

The shortest side is across from the
___________________ angle.
Example 3
Which angle is the largest in each triangle?
B
4
S
C
9
10
11
7
T
U
9
A
9
Two Triangle Inequality,
also known as
The _________________
Theorem
T
P
U
S
Q
R
If R is greater than Q then TU is _________ than PS.
Note: The angle must be _______________ the marked
sides.
Example 4
If AB = FE and AC = FG, what is true about BC and EG?
B
E
65
C
A
70
F
G
Summary/Reflection: Which side is the longest?
C
B
55
A
70
60
D
30 60
50
E
10
Section: 3-4
Name:
Topic: The Polygon Angle-
Class: Geometry 1A
Sum Theorem
Period:
Standard:
Date:
Polygon
Sketch
Number of
sides
Number of
triangles
formed
Sum of
angle
measures
Number of
interior
angles
If it was a
regular
polygon,
measure of
each int.
angle
Number of
exterior
angles
Sum of
measure of
exterior
angles
Triangle
4
360
3
6
Heptagon
8
11
Angle-Sum Theorem
One Angle of a
Regular Polygon
Interior Angles of a Polygon
Exterior Angles of a Polygon
Names of Polygons
Number of Sides
Name of Polygon
3
4
5
6
7
8
9
10
11
12
Example
1) If the measure of one interior angle of a regular polygon is
144, what is the name of the polygon?
12
2) The measure of an exterior angle of a regular polygon is 36
degrees. Name the polygon.
3) find the measure of one interior and one exterior angle in a
36-gon.
4) Solve for x
x
2x
120
100
2x
Summary/Reflection: If you forget the formulas above, explain how could you determine the
sum of the angles of a dodecagon?
13