Transcript Lesson 4 PPT

Name:________________________________________________________________________________Date:_____/_____/__________
Use the percent proportion formula for the following
%
𝒑𝒂𝒓𝒕
percentage problems (
=
):
𝟏𝟎𝟎
𝒘𝒉𝒐𝒍𝒆
1) Jack spent 20% of
his savings at the
store. If he spent
$45, how much did
he have in his savings
to begin with?
2) Sarah has 30
beanie boo stuffed
animals. She decides
to give 40% to
charity. How many
does she give away?
Choose the correct proportion:
Choose the correct proportion:
𝐀.
20
100
=
45
x
B.
20
100
= 45
x
𝐀.
40
100
=
B.
40
100
= 30
Choose the correct proportion:
𝐀.
18
100
=
42
x
B.
20
100
= 42
x
Set proportion up AND SOLVE:
=
30
x
x
Watch out for 2step problems . . .
Tax, Tip, Discounts:
4) Andrew and a
lady friend are out to
dinner. The bill is
$42. If Andrew
wants to leave an
18% tip, how much
will his tip be?
3) 12 out of 21 total
kids in the class have
a TV in their room.
What percent is this?
5) Gabby and Olivia
are shopping. Gabby
sees some sunglasses
that are originally
$35, but are on sale
for 40% off. What is
the sale price?
6) Alex is at Party
City for some fiesta
supplies. His
subtotal is $44.99. If
the sales tax is 6%,
what is his total?
Set proportion up AND SOLVE:
Set proportion up AND SOLVE:
=
=
Today’s Lesson:
What:
similar Figures
Why:
To use proportions to solve problems
involving similar figures.
Vocabulary:
Similar figure– figures that are the same
size
shape, but a different ____________________.
proportional
Corresponding sides are ________________.
congruent
Corresponding angles are _______________
.
~ symbol – means “is __________________
to.”
similar
SAME shape!
DIFFERENT size!
CONGRUENT angles!
PROPORTIONAL
sides!
Identifying corresponding sides:
1) Trapezoid ABCD ~ Trapezoid WXYZ :
(one is a reflection/dilation of the other)
C
D
W
A
1.
2.
3.
4.
B
Z
X
Y
WZ .
Side AD corresponds to side _____
WX .
Side AB corresponds to side _____
XY .
Side BC corresponds to side _____
YZ .
Side CD corresponds to side _____
B
5. Angle X corresponds to angle _____
.
D .
6. Angle Z corresponds to angle _____
Identifying corresponding sides:
2) Triangle ABC ~ Triangle DEF:
(one is a rotation/dilation of the other)
B
D
E
F
A
C
1. Side AB corresponds to side _____
DE .
2. Side AC corresponds to side _____
DF .
3. Side BC corresponds to side _____
EF .
4. Angle A corresponds to angle _____
.
D
5. Angle B corresponds to angle _____
.
E
Corresponding angles
are CONGRUENT!
If Angle B measures 35 degrees, then
what is the measure of angle E? _____
35°
Solve for a missing side length:
1) Trapezoid ABCD is similar to trapezoid
WXYZ (one is a reflection/dilation of the
other). Solve for the missing side-length.
C
D
12.5 cm
W
2 cm
X
?
A
5 cm
Write corresponding
sides as a ratio on
each side of the
proportion . . .
Z
B
𝟓
𝟐
=
Y
𝟏𝟐.𝟓
𝐱
5x = 25
5
5
x = 5 cm
Notice that this is
BIG on top and
SMALL on bottom!
Solve for a missing side length:
2) Triangle ABC is similar to triangle DEF
(one is a rotation/dilation of the other). Solve
for the missing side-length.
B
D
F
7.2 cm
A
C
x = 5 cm
4 cm
E
Solve for a missing side length:
3) 2 Similar Triangles – What is the value
of “x”?
x
16 in.
x = 19.2 in.
10 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.
Video to accompany tree/shadow
problem in your
notes (Problem #5):
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
45 ft
15 ft
x = 28.5 ft.
Time for . . .
Similar figure SPEED “DATING”!
Teacher will give
directions . . .
homework
IXL: X.13
END OF LESSON
The next slides are student copies of the notes and
handouts for this lesson. These were handed out in
class and filled-in as the lesson progressed.
NAME:
Math-7 NOTES
What:
similar Figures
Why:
To use proportions to solve problems involving similar figures.
DATE: ______/_______/_______
Vocabulary:
Similar figure – figures that are the same shape, but a different _________.
Corresponding sides are __________________________.
Corresponding angles are _________________________ .
~ symbol – means “is ___________________ to.”
SAME shape!
DIFFERENT size!
CONGRUENT angles!
PROPORTIONAL sides!
Identifying corresponding sides:
1)
Trapezoid ABCD ~ Trapezoid WXYZ :
(one is a reflection/dilation of the other)
W
A
2)
1.
2.
3.
4.
C
D
B
X
Z
Y
Side AD corresponds to side _____ .
Side AB corresponds to side _____ .
Side BC corresponds to side _____ .
Side CD corresponds to side _____ .
5. Angle X corresponds to angle _____ .
6. Angle Z corresponds to angle _____ .
Triangle ABC ~ Triangle DEF:
(one is a rotation/dilation of the other)
B
D
F
E
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 _____ .
A
C
If Angle B measures 35 degrees, then
What is the measure of Angle E? _____
Solve for a missing side length:
1)
Trapezoid ABCD is similar to trapezoid D
WXYZ (one is a reflection/dilation of the
other). Solve for the missing
side-length.
C
12.5 cm
W
2 cm
X
?
A
2) Triangle ABC is similar to triangle DEF
(one is a rotation/dilation of the other). Solve
for the missing side-length.
5 cm
B
B
Y
Z
D
4 cm
E
F
7.2 cm
C
A
3)
2 Similar Triangles – What is the value of “x”?
x
16 in.
10 in.
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?
x
9.5 ft
45 ft
15 ft
NAME:___________________________________________________________________________
DATE: ______/_______/_______
For the problems that require a proportion (solving for missing side-length), use below scratch space.
HOWEVER, some problems are asking for a missing angle. These do NOT require a proportion, and therefore
do NOT require scratch:
Example:
Answer :
This type uses
a proportion.
𝒔𝒎𝒂𝒍𝒍
𝒃𝒊𝒈
𝟏
𝟔
=
𝟐 𝒖
𝟏𝒖
𝟏
=
𝟏𝟐
𝟏
u = 12
Example:
This type does NOT
require a
proportion, so you
do not have to
show work!
Answer :
113°
because corresponding
angles are CONGRUENT!!
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NAME:_______________________________________________________________________________ DATE: ______/_______/_______
“Similar Figures”