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- is a flat surface thatextends in all directions .
Objective - To identify angles as vertical, adjacent, complementary and supplementary.
Plane
Parallel Lines
AB
CD
AB CD���������������������������������������� ���
- Lines in the same plane that do not intersect.
Intersecting Lines
AB
C
D
Vertical Angles - Formed by intersecting lines.
Opposite angles (vertical angles) are always congruent.
Adjacent Angles -Angels that share a commonvertex and side.
Complementary Angles
ab
- Angles whosesum is 90 .
m a m b 90
x y
m x m y 90
Complementary angles may notbe adjacent.
Find the measure of the missing angle.
x
x 40 90
40
40 40
x 50
x 50
Find the complement of the angle measures below.
1) 20
2) 59
3) 50
4) 62
5) 15
6) 57
7) 43
8) 100
70
31
40
28
75
33
47
Has no complement
Supplementary Angles
kt
- Angles whosesum is 180 .
m k m t 180
b c
m b m c 180
Supplementary angles may notbe adjacent.
Find the measure of the missing angle.
x
x 50 180
50
50 50
x 130
x 130
y 137 180 137 137
y 43
y 43
y 137
Find the supplement of the following...
1) 18
2) 104
3) 31
4) 75
5) 148
6) 62
7) 159
8) 179
162
76
149
105
32
118
21
1
Find the missing angles.
1) 2)
115x
yz
m x 65m y 115m z 65
A
D
CE
B
m ABC 133
m CBD 47m EBD 133
47
Every triangle has angles whose sum equals 180 .
ab
c m a m b m c 180
Solve for x.
x
85
60
m x 85 65 180 x 150 180
150 150 x 30
Objective - To use the sum of the angles of a triangle to solve problems.
Find the missing angle.
1) 2)
x 30
110
mx110 30 180
x 145180 145 145
x 35
mx 35
y
27
14
my14 27 180
y 41180 41 41
y 139
my139
Two angles of a triangle are given. Find the third angle.
1) 3)40 , 70 46 , 79
180o 40o 70o
70o
180o 46o 79o
55o
2) 4)126 , 36 101 , 12
180o 126o 36o
18o
180o 101o 12o
67o
Decide whether a triangle can have the given angle measures.
1) 3)145 , 20 , 15 57 , 44 , 79
145o 20o 15o 180o
180o 180o
YES
57o 44o 79o 180o
180o 180o
YES
2) 4)34 , 116 , 36 43 , 101 , 35
34o 116o 36o 180o
186o 180o
NO
43o 101o 35o 180o
179o 180o
NO
Objective - To classify triangles.
- All anglesless than 90 .
- Only Oneangle equal to 90 .
Triangle Names
AngleName
SideName
Acute Right - Only Oneangle more than 90 .Obtuse
- All three sides equal.Equilateral - Two
sides equal.Isosceles - No
equal sides.Scalene
Name each triangle below.
1)
2)
3)
4)
7 7
11Obtuse Isosceles
Acute Equilateral
3
4
5
Right Scalene
3
9
8
Obtuse Scalene
Angle-Side Relationships
Sides opposite congruent angles are congruent.
Angles opposite congruent sides are congruent.
10 10
10
7 7
11
Name each triangle below.
5)
6)
7)
8)
Obtuse IsoscelesAcute Isosceles
6
6
Right Scalene
2
8
5
Acute Scalene
512
13
Use the diagram below to name the following.
1) Acute Equilateral Triangle
2) Right Scalene Triangle
3) Acute Isosceles Triangle
4) Obtuse Scalene Triangle
A
B C
D
EF
12
5
13 13
10
13
13
8
18
BCE
ABF
BEF
CDE
Quadrilateral - Four sided figure.
Parallelogram - A quadrilateral with two sets ofparallel sides.
Objective - To identify and describe the properties of quadrilaterals.
Properties of Parallelograms.
Opposite sides have the same length.
Properties of Parallelograms.
Opposite angels have the same measure.
Rectangle - A parallelogram that has four right angles.
Square - A rectangle will all sides the same length.
Quadrilateral4 sided figure
Parallelogram
Two sets of parallelsides
RectangleParallelogram with right angles
SquareRectangle with equalsides
Give all the names that apply to the figure below.Circle the most specific name.
1)
2)
3)
4)
Parallelogram, Quadrilateral
Quadrilateral
6
10
6 68
14
7
7Quadrilateral, Parallelogram
, Square
3 3
3 3
Quadrilateral, Parallelogram
Rectangle,
Find the measures of x an y in each figure.
1)
2)
3)
4)
x = 4, y = 8
x = 75, y = 105
4
8
x y
75105
9
9x = 9, y = 9
x = 10, y = 120
x
y
x
y
x
y 10120
Find the sum of the measures of the angles and theperimeter.
75
Sum of the angles =
26A
12
105
B C
D
75105
105o75o105o75o 360o
Perimeter =
12
26
12 261226 76
