7.5: Using Proportional Relationships

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Transcript 7.5: Using Proportional Relationships

Happy Monday!
Take Out: Your Perspective Drawings
HW #5 : Pg. 491 #1-6, 12-14, 20-23; p 508 #6
Updates: Unit 4 Part 1 Test
( 7.1-7.6 ) next week. I will tell you the date
Remember: You can do quiz corrections if you come in
during tutorial! ALSO, ask for help during
Perspective Drawings
7.5: Using Proportional Relationships
Quiz Master
7.1-7.3 Quiz
You need to make it up TODAY or you will receive a ZERO!
Perspective Drawings
You may wonder how these drawings relate to Geometry?
Take out a ruler. Measure lines that correspond to the same
thing in your picture.
Are the measurements proportional?
7.5: Using Proportional
You will be able to:
(1) Use ratios to make indirect measurements.
(2) Use scale drawings to solve problems.
Thales is known as the first Greek scientist,
engineer, and mathematician.
Legend says that he was the first to determine
the height of the pyramids in Egypt!
He did this by examining the
shadows made by the Sun. He
considered three points: the top
of the pyramids, the lengths of
the shadows, and the bases.
With your table, discuss the following questions.
(1) What appears to be true about the corresponding angles in the
two triangles?
(2) If the corresponding sides are proportional, what could you
conclude about the triangles?
Similarity is often used to measure heights and lengths of
objects, build scale models, maps, and blueprints.
Similarity is the one of the most useful applications
of geometry.
Indirect Measurement
Indirect Measurement
o Any method that uses formulas, similar figures, and/or
proportions to measure an object.
o Thales used indirect measurement to measure his height and the
length of his shadow and compared it with the length of the
shadow cast by the pyramid to find the height of the pyramid.
7-5 Using Proportional Relationships
If Thales is 5ft tall, his shadow is
7 ft long, and the length of the
pyramids shadow is 100 ft long,
how tall is the pyramid?
Example 1:
In reality, we are not all going to be measured to the
nearest ft. For example, I am 5 foot 3 inches.
Tyler wants to find the height of a telephone pole. He
measured the poles shadow and his own shadow and
then made a diagram. What is the height h of the pole?
Example 1(a) Continued…
Step 1 Divide inches/12 to see how much of a foot that
Step 2: Find h.
Example 1(b)
Drop Zone in Great America casts a shadow that is 43⅔
ft long. At the same time, a 6 ft 4 in. tall person standing
in line casts a shadow 2 ft long. What is the height of the
ride? Round to the nearest tenth.
A student who is 5 ft 6 in.
tall measured shadows
to find the height LM of a
flagpole. What is LM?
Scale Drawing
0 Represents an object as smaller than or larger than its
actual size. The drawing’s scale is the ratio of any
length in the drawing to the corresponding actual
0 For example, you did a scale on your Chapter 7
project. You showed how many cm/inches your bed
was on your picture to the actual length of your bed.
Example 2(a)
Rachel is a cartographer. She is currently making a map
of Australia. She wants to make her map scale 1-inch for
every 200 km. Australia is 4000 km wide. If her paper is
11 inches wide, can she fit a drawing of the whole
continent onto the paper? Justify your response.
Example 2(b)
An artist makes a scale drawing of a new lion enclosure
at the San Francisco Zoo. The scale is
1 in : 25 ft. On
the drawing, the length of the enclosure is 7 ¼ inches.
What is the actual length of the lion enclosure? Round
to the hundredth.
Example 2( c)
The rectangular central chamber of the Lincoln
Memorial is 74 ft long and 60 ft wide. Make a scale
drawing of the floor of the chamber using a scale of 1
in.:20 ft.
3.7 in.
3 in.
Math Joke of the Day!
Q: How many seconds are there in a year?
A: Twelve. January second, February second, March
7-5 Using Proportional Relationships
We have discussed a lot about similar triangles and their side
What about similar triangles and their perimeters?
What about similar triangles and their areas?
7-5 Using Proportional Relationships
o Take 2 minutes to write down your definition of perimeter and
your definition of area.
o Lets investigate what the relationship might be between the
similarity ratio, perimeter, and area of a figure.
7-5 Using Proportional Relationships
You will have the next 8 minutes to complete the Investigation
on the back of your notes.
7-5 Using Proportional Relationships
7-5 Using Proportional Relationships
Example 3
Given that ∆LMN ~ ∆QRT, find the perimeter P and area A of ∆QRS.
∆ABC ~ ∆DEF, BC = 4 mm, and EF = 12 mm. If P = 42 mm and A =
96 mm2 for ∆DEF, find the perimeter and area of ∆ABC.
Quiz Master
Create your own word problem and solve it that
involves one of the following:
o Indirect Measurement
o Scale Drawing
o Ratio of Area and Perimeter
I may use this on your test!
Exit Ticket
1Maria is 4 ft 2 in. tall. To find the
height of a flagpole, she
measured her shadow and the
pole’s shadow. What is the
height h of the flagpole?
2. A blueprint for Latisha’s
bedroom uses a scale of 1 in.:4
ft. Her bedroom on the
blueprint is 3 in. long. How
long is the actual room?
Interactive Quiz!