today’s lesson:
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Today’s Lesson:. What: similar Figures Why : To use proportions to solve problems involving similar figures. Vocabulary: Similar figure– figures that are the same shape, but a different ____________________. Corresponding sides are ________________. - PowerPoint PPT PresentationTRANSCRIPT
Today’s Lesson:
What: similar Figures
Why: To use proportions to solve problems involving similar figures.
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
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)
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)
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
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
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.
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.
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.
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.
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
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
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
Math-7 Practice/ homework“Similar Figures”
DATE: ______/_______/_______NAME:_______________________________________________________________________________