16
Today’s Lesson: What: similar Figures Why: To use proportions to solve problems involving similar figures.

Today’s Lesson: What: similar Figures Why: To use proportions to solve problems involving similar figures. What: similar Figures Why: To use proportions

Embed Size (px)

Citation preview

Page 2: Today’s Lesson: What: similar Figures Why: To use proportions to solve problems involving similar figures. What: similar Figures Why: To use proportions

Vocabulary:

Similar figure– figures that are the same shape, but a different ____________________.

Corresponding sides are ________________.

Corresponding angles are _______________ .

~ symbol – means “is __________________ to.”

size

proportional

congruent

SAME shape!DIFFERENT size!

CONGRUENT angles!

PROPORTIONAL sides!

similar

Page 3: Today’s Lesson: What: similar Figures Why: To use proportions to solve problems involving similar figures. What: similar Figures Why: To use proportions

Identifying corresponding sides:

A B

D C

X

YZ

W

1. Side AD corresponds to side _____ .2. Side AB corresponds to side _____ .3. Side BC corresponds to side _____ .4. Side CD corresponds to side _____ .

5. Angle X corresponds to angle _____ .6. Angle Z corresponds to angle _____ .

WZWX

XYYZ

BD

1) Trapezoid ABCD ~ Trapezoid WXYZ : (one is a reflection of the other)

Page 4: Today’s Lesson: What: similar Figures Why: To use proportions to solve problems involving similar figures. What: similar Figures Why: To use proportions

Identifying corresponding sides:

1. Side AB corresponds to side _____ .2. Side AC corresponds to side _____ .3. Side BC corresponds to side _____ .

4. Angle A corresponds to angle _____ .5. Angle B corresponds to angle _____ .

DE

B

A C

ED

F

DF

EF

D

E

2) Triangle ABC ~ Triangle DEF: (one is a rotation of the other)

Page 5: Today’s Lesson: What: similar Figures Why: To use proportions to solve problems involving similar figures. What: similar Figures Why: To use proportions

Solve for a missing side length:

1) Trapezoid ABCD is similar to trapezoid WXYZ (one is a reflection of the other). Solve for the missing side-length.

A B

D C

X

YZ

W

5 cm

2 cm12.5 cm

?

x = 5 cm

Page 6: Today’s Lesson: What: similar Figures Why: To use proportions to solve problems involving similar figures. What: similar Figures Why: To use proportions

Solve for a missing side length:

2) Triangle ABC is similar to triangle DEF (one is a rotation of the other). Solve for the missing side-length. B

A C

ED

F9 cm

?

7.2 cm

4 cm

x = 5 cm

Page 7: Today’s Lesson: What: similar Figures Why: To use proportions to solve problems involving similar figures. What: similar Figures Why: To use proportions

Solve for a missing side length:

3) 2 Similar Triangles – What is the value of “x”?

12 in

.

10 in.16 in.

x

x = 19.2 in.

Page 8: Today’s Lesson: What: similar Figures Why: To use proportions to solve problems involving similar figures. What: similar Figures Why: To use proportions

Solve for a missing side length:

4)Scenario: The length and width of a rectangular box are 24 in. and 14 in. respectively. Another rectangular box has a length of 12 in. What is the smaller box’s width?

x = 7 in.

Page 9: Today’s Lesson: What: similar Figures Why: To use proportions to solve problems involving similar figures. What: similar Figures Why: To use proportions

Solve for a missing side length:

5) A 9.5 ft. tall tree casts a shadow 15 ft. in

length. A nearby building casts a shadow that is 45 ft. in length. How tall is the building?

x

9.5 ft

15 ft45 ft

x = 28.5 ft.

Page 10: Today’s Lesson: What: similar Figures Why: To use proportions to solve problems involving similar figures. What: similar Figures Why: To use proportions

END OF LESSON

The next slides are student copies of the notes for this lesson. These notes were handed out in class

and filled-in as the lesson progressed.

NOTE: The last slide(s) in any lesson slideshow (entitled “Practice Work”)

represent the homework assigned for that day.

Page 11: Today’s Lesson: What: similar Figures Why: To use proportions to solve problems involving similar figures. What: similar Figures Why: To use proportions

Identifying corresponding sides:

Math-7 NOTES DATE: ______/_______/_______What: similar Figures

Why: To use proportions to solve problems involving similar figures. NAME:

Vocabulary:Similar figure – figures that are the same shape, but a different _________.

Corresponding sides are __________________________.

Corresponding angles are _________________________ .

~ symbol – means “is ___________________ to.

A B

D C

X

YZ

W

1) Trapezoid ABCD ~ Trapezoid WXYZ : (one is a reflection of the other)

2) Triangle ABC ~ Triangle DEF: (one is a rotation of the other)

1. Side AD corresponds to side _____ .2. Side AB corresponds to side _____ .3. Side BC corresponds to side _____ .4. Side CD corresponds to side _____ .

5. Angle X corresponds to angle _____ .6. Angle Z corresponds to angle _____ .

1. Side AB corresponds to side _____ .2. Side AC corresponds to side _____ .3. Side BC corresponds to side _____ .

4. Angle A corresponds to angle _____ .5. Angle B corresponds to angle _____ .

SAME shape!DIFFERENT size!

CONGRUENT angles!PROPORTIONAL

sides!

B

A C

ED

F

Page 12: Today’s Lesson: What: similar Figures Why: To use proportions to solve problems involving similar figures. What: similar Figures Why: To use proportions

Solve for a missing side length:

1) Trapezoid ABCD is similar to trapezoid WXYZ (one is a reflection of the other). Solve for the missing side-length.

2) Triangle ABC is similar to triangle DEF (one is a rotation of the other). Solve for the missing side-length.

3) 2 Similar Triangles – What is the value of “x”?

4) Scenario: The length and width of a rectangular box are 24 in. and 14 in. respectively. Another rectangular box has a length of 12 in. What is the smaller box’s width?

5) A 9.5 ft. tall tree casts a shadow 15 ft. in length. A nearby building casts a shadow that is 45 ft. in length. How tall is the building?

A B

D C

X

YZ

W

5 cm

2 cm12.5 cm

?

x

9.5 ft

15 ft45 ft

12 in

.10 in.16 in.

x

B

A C

ED

F

9 cm

?

7.2 cm

4 cm

Page 13: Today’s Lesson: What: similar Figures Why: To use proportions to solve problems involving similar figures. What: similar Figures Why: To use proportions

Find the value of “x” in the following similar figures:

1)

2)

3)

Math-7 Classwork“Similar Figures”

DATE: ______/_______/_______NAME:_____________________________________________________________________________

E

D

F

4.5 ft

x

CA

3 ft

4 ft

B

A

B C

D

14 ft12 ft

F

G

H

J

x

18 ft

L M

N O

20 in

12 in

Q R

S T

15 in

x

Page 14: Today’s Lesson: What: similar Figures Why: To use proportions to solve problems involving similar figures. What: similar Figures Why: To use proportions
Page 15: Today’s Lesson: What: similar Figures Why: To use proportions to solve problems involving similar figures. What: similar Figures Why: To use proportions

Math-7 Practice/ homework“Similar Figures”

DATE: ______/_______/_______NAME:_______________________________________________________________________________

Page 16: Today’s Lesson: What: similar Figures Why: To use proportions to solve problems involving similar figures. What: similar Figures Why: To use proportions