WELCOME TO

MATH 6

Today’s subject is:

Proportions and Similar Figures

OBJECTIVES FOR THIS LESSON:

Each student will:

1- Use proportions to determine if two figures are similar.

2-Use proportions to make similar figures.

3-Use proportions to find the length of corresponding sides of similar figures.

Matching sides of two or more polygons are called corresponding sides, and matching angles are called corresponding angles.

Key Vocabulary

𝑹

𝑸

𝑺𝑩𝑪

𝑨

Use ratios to determine if two figures are similar.

𝟖𝐢𝐧

𝟕𝐢𝐧 10

24

21 𝟑𝟎𝐢𝐧

𝐐

𝐒

𝐑

𝐅𝐃

𝐄

24

21 𝟑𝟎𝐢𝐧

𝐐

𝐒

𝐑𝟖𝐢𝐧

𝟕𝐢𝐧 10

𝐅𝐃

𝐄

DE corresponds to RS.EF corresponds to SQQR corresponds to FD

𝐷𝐸𝑅𝑆

=𝐸𝐹𝑆𝑄

=𝐹𝐷𝑄𝑅

24

21 𝟑𝟎𝐢𝐧

𝐐

𝐒

𝐑𝟖𝐢𝐧

𝟕𝐢𝐧 10

𝐅𝐃

𝐄

721

=1030

=824

24

21 𝟑𝟎𝐢𝐧

𝐐

𝐒

𝐑𝟖𝐢𝐧

𝟕𝐢𝐧 10

𝐅𝐃

𝐄

Similar figures have the same shape, but not necessarily the same size. Similar figures have corresponding sides and corresponding angles.

The symbol ~ means “is similar to.” ABC ~ QRS.

𝑺

𝑹

𝑸𝑨 𝑪

𝑩

If two figures are similar, then their corresponding angles are congruent, and the lengths of the corresponding sides are proportional.

𝒌

𝒉

𝒚

𝒙𝒊

𝒋

𝒘

𝒛

To find out if triangles are similar, determine whether the ratios of the lengths of their corresponding sides are proportional. If the ratios are proportional, then the corresponding angles must have equal measures.

Similar figures have two properties:1. The corresponding angles have

equal measures.2. The lengths of the corresponding

sides are in proportion.

In figures with four or more sides, it is possible for the corresponding side lengths to be proportional and the figures to have different shapes.

To find out if these figures are similar, first check that their corresponding angles have equal measures.

10

10 10

107 7 7 7

When you know two figures are similar, you can find the measure of a missing side by setting up a proportion.

Parallelogram ABCD ~ Parallelogram EFGH. Find the value of x.

2418

24

𝑥

Create a proportion: 2418

16x

Guided Practice

Identify the corresponding sides in each pair of triangles. Then use ratios to find whether the triangles are similar.

Guided Practice #1

6

9 12

𝐅𝐃

𝐄3

20

4𝐐

𝐒

𝐑

Identify the corresponding sides in each pair of triangles. Then use ratios to find whether the triangles are similar.

Guided Practice #2

𝑺

𝑹

𝑸𝑨

𝑩

𝑪

715

20

28

5

3

Use the properties of similarity to determine whether the figures are similar.

Guided Practice #3

𝑩

𝑪

𝑨

𝑫

𝑭

𝑮

𝑬

𝑯6

33

62 2

4

4

Use the properties of similarity to determine whether the figures are similar.

Guided Practice #4

𝒊

𝒋

𝒘

𝒛

𝒙𝒉

y𝒌

14

24

14

101010

18

9

Guided Practice #5These two triangles are similar. Use a proportion to find the length of the missing side.

𝟐

𝟓𝒚

𝟏𝟔

𝟖

𝟐𝟎

Guided Practice #5 Notes to instructor

Show how the measure of y = 4.

Independent Practice

𝒊

𝒋

𝒘

𝒛

𝒙𝒉

y𝒌

25

24

25

10

1818

15

6

Independent Practice #1Use the properties of similarity to determine whether the figures are similar.

Identify the corresponding sides in each pair of triangles. Then use ratios to find whether the triangles are similar.

Independent Practice #2

𝑺

𝑹

𝑸𝒂𝒄

𝒃

𝟔

𝟒𝟕

𝟖𝟏𝟎𝟏𝟒

Independent Practice #3Identify the corresponding sides in each pair of triangles. Then use ratios to find whether the triangles are similar.

𝟏𝟐

𝟏𝟓 𝟏𝟖 𝟏𝟐𝟏𝟎

Independent Practice #4Identify the corresponding sides in each pair of triangles. Then use ratios to find whether the triangles are similar.

𝟏𝟐

𝟏𝟎𝟏𝟎 𝟏𝟓

𝟏𝟖

𝟏𝟓

Independent Practice #5These two triangles are similar. Use a proportion to find the length of the missing side.

𝒏

𝟏𝟓𝟏𝟐

𝟏𝟔

𝟖

𝟐𝟎

INDEPENDENT PRACTICE #6These two triangles are similar. Use a proportion to find the length of the missing side.

𝒔

𝟔𝟏𝟐

𝟒

𝒊𝒋

𝒘

𝒛

𝒙𝒉

y𝒌

18

24

18

12

24

24

24

6

Independent Practice #7Use the properties of similarity to determine whether the figures are similar.

𝑪𝑩𝑨

𝑫𝑭𝑬G𝑯

Independent Practice #8Write a proportion for corresponding sides which would make these similar figures.

INDEPENDENT PRACTICE #9Write a proportion for corresponding sides which would make these similar figures.

Trapezoid EFGH ~ trapezoid MNOP

Independent Practice #10Write a proportion for corresponding sides which would make these similar figures.

CONCLUSION

In this lesson we:

1- Used proportions to determine if two figures are similar.

2-Used proportions to make similar figures.

3-Used proportions to find the length of corresponding sides of similar figures.

Assignments-1. Complete the attached exercise

entitled, “Worksheet 4.2: Proportions and Similar Figures.”

2. Look at Math website for more information about Proportions and similar figures.

http://www.math.com/school/subject3/lessons/S3U3L2GL.html

Assignments-

3. Here is one more website to check out for more information. This one actually has a quiz at the end. You can test yourself to find out how much of this you have retained. The website is http://studyjams.scholastic.com/studyjams/jams/math/geometry/similar-figures.htm

See you next time!

See you next tim

e!S

ee y

ou n

ext t

ime!

See you next time!