Unit5

- is a flat surface thatextends in all directions .

Objective - To identify angles as vertical, adjacent, complementary and supplementary.

Plane

Parallel Lines

AB

CD

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- 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