When two objects are congruent, they have the same shape and size. Two objects are similar if they have the same shape, but different sizes. Their

When two objects are congruent, they have the same shape and size.

Two objects are similar if they have the same shape, but different sizes.

Their corresponding parts are all proportional.

Any kind of polygon can have two that are similar to each other.

When two objects are congruent, they have the same shape and size.

Two objects are similar if they have the same shape, but different sizes.

Their corresponding parts are all proportional.

Any kind of polygon can have two that are similar to each other.

SimilaritySimilarity

Examples: 2 squares that have different lengths of sides.

2 regular hexagons

Examples: 2 squares that have different lengths of sides.

2 regular hexagons

SimilaritySimilarity

Similar Polygons (7-2)Similar Polygons (7-2)

Characteristics of similar polygons:1. Corresponding angles are congruent

(same shape)

2. Corresponding sides are proportional

(lengths of sides have the same ratio)

ABCD ~ EFGH

Vertices must be listed in order when naming

Characteristics of similar polygons:1. Corresponding angles are congruent

(same shape)

2. Corresponding sides are proportional

(lengths of sides have the same ratio)

ABCD ~ EFGH

Vertices must be listed in order when naming


ABCD ~ EFGH

Complete the statements.

ABCD ~ EFGH

Complete the statements.

115

65

H

F

G

B

C D

A

E

AB

EF =

BC

?

HG

DC =

FG

?

mF = ?

mC = ?


Determine whether the parallelograms are similar. Explain.

Determine whether the parallelograms are similar. Explain.

44

2

2

22

1

1

114

59


Scale factor- ratio of the lengths of two corresponding sides of two similar polygons

The scale factor can be used to determine unknown lengths of sides

Scale factor- ratio of the lengths of two corresponding sides of two similar polygons

The scale factor can be used to determine unknown lengths of sides


If ABC ~ YXZ, find the scale factor of the large triangle to the small and find the value of x.

scale factor = 5/2 x= 16

If ABC ~ YXZ, find the scale factor of the large triangle to the small and find the value of x.

scale factor = 5/2 x= 16

x

12

A

BC

40

30Z

X

Y

Example from Similar Polygons Worksheet

Example from Similar Polygons Worksheet

Are the two polygons shown similar? Corresponding angles must be congruent All pairs of corresponding sides must be

proportional (same scale factor)

Are the two polygons shown similar? Corresponding angles must be congruent All pairs of corresponding sides must be

proportional (same scale factor)

Example from Using Similar Polygons Worksheet

Example from Using Similar Polygons Worksheet

Given two similar polygons. Find the missing side length. Redraw one of the polygons so corresponding

sides match up (if needed) Determine the scale factor Set up a proportion and solve for the missing

side length

Given two similar polygons. Find the missing side length. Redraw one of the polygons so corresponding

sides match up (if needed) Determine the scale factor Set up a proportion and solve for the missing

side length


Homework Similar Polygons worksheet #1-17

odd Using Similar Polygons worksheet

#1-15 odd

Homework Similar Polygons worksheet #1-17

odd Using Similar Polygons worksheet

#1-15 odd

Scale DrawingScale Drawing

Problem 2 on p.443

Complete Similarity Application Problems

More practice

p.444 #9, 13, 15, 19, 23, and 25

Problem 2 on p.443

Complete Similarity Application Problems

More practice

p.444 #9, 13, 15, 19, 23, and 25

Similar Triangles (7-3)Similar Triangles (7-3)

AA ~ Postulate – If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

AA ~ Postulate – If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

A' C'

B'

A

B

C


SAS ~ Theorem – If an angle of one triangle is congruent to an angle of a second triangle, and the sides including the two angles are proportional, then the triangles are similar.

SAS ~ Theorem – If an angle of one triangle is congruent to an angle of a second triangle, and the sides including the two angles are proportional, then the triangles are similar.

A' C'

B'

A

B

C


SSS ~ Theorem – If the corresponding sides of two triangles are proportional, then the triangles are similar.

SSS ~ Theorem – If the corresponding sides of two triangles are proportional, then the triangles are similar.

A' C'

B'

A

B

C


8

6

12

9

I

E

F

G

H


Are the triangles similar? If so, write a similarity statement and name the postulate or theorem you used. If not, explain.

No the vertical angle is not between the two pairs of proportional sides.

Are the triangles similar? If so, write a similarity statement and name the postulate or theorem you used. If not, explain.

No the vertical angle is not between the two pairs of proportional sides.

86

12

9

I

E

F

G

H


O

J K

L M


Find the value of x. Find the value of x.

x

25

40

10R S

T

U V

W

Indirect Measurement (7-3)Indirect Measurement (7-3)

When a 6 ft man casts a shadow 18 ft long, a nearby tree casts a shadow 93 ft long. How tall is the tree?

When a 6 ft man casts a shadow 18 ft long, a nearby tree casts a shadow 93 ft long. How tall is the tree?

HomeworkHomework

7-4 A Postulate for Similar Triangles (AA) worksheet #1-12 all

7-5 Theorems For Similar Triangles (SSS and SAS) worksheet #1-6 all

Similar Triangles Worksheet (all three methods)

7-4 A Postulate for Similar Triangles (AA) worksheet #1-12 all

7-5 Theorems For Similar Triangles (SSS and SAS) worksheet #1-6 all

Similar Triangles Worksheet (all three methods)

Similarity in Right Triangles (7-4)Similarity in Right Triangles (7-4)

Theorem: The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other.

Theorem: The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other.

DA

B

C


Geometric mean

For any two positive numbers a and b, x is the geometric mean if

Another way to find the geometric mean:

Geometric mean

For any two positive numbers a and b, x is the geometric mean if

Another way to find the geometric mean:

abx

b

x

x

a


Find the geometric mean of 32 and 2.





2

6

xQ N

O

P


5

x

4 BY

Z

A


HomeworkHomework

8-1 worksheet #24-31 all 8-1 worksheet #24-31 all

Proportions in Triangles (7-5)Proportions in Triangles (7-5)

Side-Splitter Theorem – If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

Side-Splitter Theorem – If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

y

6

10

12E

A

B

C

D


Solve for x.

x = 9

Solve for x.

x = 9

x + 1

x + 6

x - 3xO

K

L

M

N


Corollary: If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.

Corollary: If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.

b d

ca


Solve for x.

x = 24

Solve for x.

x = 24

21

14

x

16


Triangle-Angle-Bisector Theorem – If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.

x = 18

Triangle-Angle-Bisector Theorem – If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.

x = 18

30

x

24

40

J

G H

I


Solve for x.

x = 11.25

Solve for x.

x = 11.25

12.5

9x

10

NK

L

M

HomeworkHomework

7-6 Proportional Lengths worksheet Proportional Parts in Triangles and Parallel

Lines worksheet

p.475 #9-12, 15-22 Study for test

7-6 Proportional Lengths worksheet Proportional Parts in Triangles and Parallel

Lines worksheet

p.475 #9-12, 15-22 Study for test

Documents

When two objects are congruent, they have the same shape and size. Two objects are similar if they have the same shape, but different sizes. Their