1 / 13

# Lesson 8-R - PowerPoint PPT Presentation

Lesson 8-R. Chapter 8 Review. Transparency 9-1. 5-Minute Check on Chapter 8. Complete each statement about parallelogram LMNO LM  _______ MN  _______ OLM  _______ MP  _______ Find the measure of each interior angle

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Lesson 8-R' - lola

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Lesson 8-R

Chapter 8 Review

5-Minute Check on Chapter 8

• Complete each statement about parallelogram LMNO

• LM  _______

• MN  _______

• OLM  _______

• MP  _______

• Find the measure of each interior angle

• What is the measure of each interior angle of a regular pentagon?

ON

L

M

LO

P

ONM

O

N

PO

A

B

(8y - 5)°

(4y + 5)°

A = C = 65°

B = D = 115°

(4y + 5)°

(8y - 5)°

D

C

Standardized Test Practice:

A

90°

B

108°

C

120°

D

135°

B

Click the mouse button or press the Space Bar to display the answers.

### Angles in Convex Polygons

Interior angle + exterior angle = 180°

They are a Linear Pair

Sum of Interior angles, S = (n-2)  180°

One Interior angle = S / n = (n-2)  180°/n

Sum of Exterior angles = 360°

Number of sides, n = 360° / Exterior angle

Interior angle

Exterior angle

Find the sum of the interior angles in a 16-gon

Find the sum of the exterior angles in a 16-gon

Find the number of sides of a polygon if an interior angle is 140°.

Polygons

Parallelograms

Kites

Trapezoids

IsoscelesTrapezoids

Rectangles

Rhombi

Squares

Trapezoids

IsoscelesTrapezoids

Parallelograms

Rhombi

Kites

Rectangles

Squares

4 sided polygon

4 interior angles sum to 360

4 exterior angles sum to 360

Parallelograms

Trapezoids

Bases Parallel

Legs are not Parallel

Leg angles are supplementary

Median is parallel to basesMedian = ½ (base + base)

Opposite sides parallel and congruent

Opposite angles congruent

Consecutive angles supplementary

Diagonals bisect each other

Rectangles

Rhombi

IsoscelesTrapezoids

All sides congruent

Diagonals perpendicular

Diagonals bisect opposite angles

Angles all 90°

Diagonals congruent

Legs are congruent

Base angle pairs congruent

Diagonals are congruent

Squares

Diagonals divide into 4 congruent triangles

35°

2y -1

25

35

3x - 8

R

S

J

K

V

16

2k°

N

L

M

U

T

4y + 4

W

P

A

B

H

Example Problems 2

In the square,

In the rectangle,

18

9z

In the rhombus,

24

t

3z

4x

z

54°

In the isosceles trapezoid

EF is a median,

2y

In the parallelogram,

P

Q

6x - 6

A

B

3x+5

6x

6z°

24

3y - 6

25

3y

2z + 6

35

E

F

3t°

8t°

y + 4

9z°

5t°

2t°

S

R

C

D

2x + 8

Find the sum of the interior angles in a 16-gon

Find the sum of the exterior angles in a 16-gon

Find the number of sides of a polygon if an interior angle is 140°.

S = (n – 2)  180 = (16 – 2)  180 = 14  180 = 2520

S = 360

Int  + Ext  = 180 so Ext  = 40

n = 360 / Ext  = 360 / 40 = 9

35°

2y -1

25

35

3x - 8

R

S

J

K

V

16

2k°

N

L

M

U

T

4y + 4

W

P

A

B

H

Example Solutions 2

2 pairs isosceles ∆

35 + 35 + x = 180

x + m = 180 (L pr)

m = 70

In the square,

In the rectangle,

18

9z

In the rhombus,

Opposite sides =

35 = 3x + 8

27 = 3x

9 = x

24

all sides =

4y + 4 = 16 = 3x – 8

4y = 12 24 = 3x

y = 3 8 = x

t

3z

4x

z

54°

2y

diagonals =

and bisected

25 = 2y – 1

26 = 2y

13 = 3

diagonals bisected

z = t

8 = t

all sides =

3z = 4x = 2y = 24

z = 8, x = 6, y = 12

diagonals 

2k = 90

k = 45

diagonals bisect angles

w = 54

isosceles legs =

y + 4 = 3y – 6

10 = 2y

5 = y

diagonals bisected

35 = 3x + 5

30 = 3x

10 = x

opposite sides =

24 = 2z + 6

18 = 2z

9 = z

isosceles leg ’s

supplementary

6z + 9z = 180

15z = 180

z = 12

diagonals bisected

3y = 6x

3y = 60

y = 20

isosceles

base ’s =

6z = m

72 = m

Consecutive ’s

supplementary

8t + 5t + 2t + 3t = 180

18t = 180

t = 10

In the isoscelestrapezoid

EF is a median,

In the parallelogram,

median = ½(sum of bases)

25 = ½(6x – 6 + 2x + 8)

50 = 6x – 6 + 2x + 8

50 = 8x + 2

48 = 8x

6 = x

P

Q

6x - 6

A

B

3x+5

6x

6z°

24

3y - 6

25

3y

2z + 6

35

E

F

3t°

8t°

y + 4

9z°

5t°

2t°

S

R

C

D

2x + 8

• Homework assignment

• Chapter 8 Review Problems

• Summary:

• Interior and Exterior angles make a linear pair (=180)

• Sum of interior angles = (n - 2)  180

• Sum of exterior angles = 360 (no matter the size)

• Number of sides = 360 / exterior angle

• Quadrilateral characteristics are very important for solving problems and verifying figures

• Reminder: Sum of triangle angles = 180

• Medians in trapezoids are similar to mid-segments

• Homework:

• study for the test