Chapter 7 Similarity and Proportion - PowerPoint PPT Presentation

1 / 66
Title:

Chapter 7 Similarity and Proportion

Description:

Chapter 7 Similarity and Proportion Express a ratio in simplest form. State and apply the properties of similar polygons. Use the theorems about similar triangles. – PowerPoint PPT presentation

Number of Views:46
Avg rating:3.0/5.0
Slides: 67
Provided by: bcp74
Category:
Tags:
Transcript and Presenter's Notes

Title: Chapter 7 Similarity and Proportion

1
Chapter 7Similarity and Proportion
• Express a ratio in simplest form.
• State and apply the properties of similar
polygons.
• Use the theorems about similar triangles.

2
7.1 Ratio and Proportion
• Objectives
• Express a ratio in simplest form
• Solve for an unknown in a proportion

3
Ratio
• A comparison between numbers

5 7
5 7 s 5 t
4
Ratio
• Always reduce ratios to the simplest form

5
Proportion
• An equation containing ratios

6
Solving a Proportion
First, cross-multiply
Next, divide by 5
7
White Board Practice
• ABCD is a parallelogram. Find the value of each
ratio.

8
White Board Practice
• AB BC

9
White Board Practice
• 5 3

10
White Board Practice

11
White Board Practice
• 1 1

12
White Board Practice
• m ? A m ? C

13
White Board Practice
• 1 1

14
White Board Practice
• AB perimeter of ABCD

15
White Board Practice
• 5 16

16
White Board Practice
• x 2 and y 3. Write each ratio in simplest
form.
• x to y

17
White Board Practice
• x 2 and y 3. Write each ratio in simplest
form.
• 2 to 3

18
White Board Practice
• x 2 and y 3. Write each ratio in simplest
form.
• 6x2 to 12xy

19
White Board Practice
• x 2 and y 3. Write each ratio in simplest
form.
• 1 to 3

20
White Board Practice
• x 2 and y 3. Write each ratio in simplest
form.
• y x
• x

21
White Board Practice
• x 2 and y 3. Write each ratio in simplest
form.
• 1
• 2

22
7.2 Properties of Proportions
• Objectives
• Express a given proportion in an equivalent form.

23
Means and Extremes
• The extremes of a proportion are the first and
last terms
• The means of a proportion are the middle terms

a b c d
24
Properties of Proportion
is equivalent to
1.
3.
2.
4.
25
That just means that you can rewrite
As any of these
1.
3.
2.
4.
26
Another Property
27
White Board Practice
• If , then 2x _______

28
White Board Practice
• If , then 2x 28

29
White Board Practice
• If 2x 3y, then

30
White Board Practice
• If 2x 3y, then

31
White Board Practice
• If , then

32
White Board Practice
• If , then

33
White Board Practice
• If , then

34
White Board Practice
• If , then

35
7.3 Similar Polygons
• Objectives
• State and apply the properties of similar
polygons.

36
Similar Polygons
• Same shape
• Not the same size ? Why?

37
• Not the same size ? Why?

Because then they would be congruent !
38
Similar Polygons ()
• All corresponding angles congruent
• ?A ? ?A
• ?B ? ?B
• ?C ? ?C

A
A
C
B
C
B
39
Similar Polygons ()
• All corresponding sides in proportion
• AB BC CA
• AB BC CA

A
A
B
C
C
B
40
The Scale Factor
• The reduced ratio between any pair of
corresponding sides or the perimeters.
• 123

12
3
41
Finding Missing Pieces
• You have to know the scale factor first to find
missing pieces.

12
3
10
y
42
White Board Practice
Find their scale factor

43
White Board Practice
• 53

44
White Board Practice
Find the values of x, y, and z

45
White Board Practice
• x 18
• y 20
• z 13.2

46
White Board Practice
Find the ratio of the perimeters

47
White Board Practice
• 53

48
7.4 A Postulate for Similar Triangles
• Objectives
• Learn to prove triangles are similar.

49
AA Simliarity Postulate(AA Post)
• If two angles of one triangle are congruent to
two angles of another triangle, then the
triangles are similar.

A
D
F
E
B
C
50
Remote Time
• T Similar Triangles
• F Not Similar

51
T Similar TrianglesF Not Similar
52
T Similar TrianglesF Not Similar
53
T Similar TrianglesF Not Similar
54
T Similar TrianglesF Not Similar
55
7-5 Theorems for Similar Triangles
• Objectives
• More ways to prove triangles are similar.

56
SAS Similarity Theorem (SAS)
• If an angle of a triangle is congruent to an
angle of another triangle and the sides including
those angles are proportional, then the triangles
are similar.

A
D
F
E
B
C
57
SSS Similarity Theorem (SSS)
• If the three sides of one triangle are
proportional to the three sides of another
triangle, then the triangles are similar.

A
D
F
E
B
C
58
Homework Set 7.5
• 7-5 1-19 odd
• WS PM 40

59
7-6 Proportional Lengths
• Objectives
• Apply the Triangle Proportionality Theorem and
its corollary
• State and apply the Triangle Angle-bisector
Theorem

60
Divided Proportionally
• If points are placed on segments AB and CD so
that , then we say that these
• segments are divided proportionally.

B
D
X
Y
A
C
See It!
61
Theorem 7-3
• If a line parallel to one side of a triangle
intersects the other two sides, it divides them
proportionally.

Y
See It!
B
A
X
Z
62
Corollary
• If three parallel lines intersect two
transversals, they they divide the transversal
proportionally.

R
W
S
X
T
Y
See It!
63
Theorem 7-4
• If a ray bisects an angle of a triangle, then it
divides the opposite side into segments
proportional to the other two sides.

Y
See It!
W
X
Z
64
Construction 12
Given a segment, divide the segment into a given
number of congruent segments. Given Construct S
teps
65
Construction 13
Given three segments, construct a fourth segment
so that the four segments are proportional. Given
Construct Steps
66
Homework Set 7.6
• WS PM 41
• WS Constructions 12 and 13
• 7-6 1-23 odd
• Quiz next class day