Real Life Similarity
Questions of the Day:
Lesson 28
1.) Are the triangles similar?
2.) Line ℓ has the equation y=-5x+2. Write the equation
of the image of ℓ after a dilation with a scale factor of 3,
centered at the origin.
3) Find SI if PI = 28, TI = 20, and NI = 24
4.) The transformation of triangle IPO with I(-20, 28),
P(-32, 4) and O(-48, -40) after a dilation is I’(5, -7),
P’(8, -1) and O’(12, 10). What is the scale factor of the
dilation?
Class Discussion:
- ________________
__________________: used to ____________ ______________,
_________________, or __________________ that are too ______________ to be measured with
measuring tools.
-
uses _______________ ___________ and _________________
find the measurements.
How to set up a proportion:
EX: Comparing real life measurements and similar triangles:
Both the observer and the building are casting
shadows that can be measured. The observer’s
height can also be measured. Indirect measure
can be used to find the height of the building.
___________lengths to
If the figure is labeled with just heights and
lengths, notice the similar triangles.
Discussion:
1.) What triangles are similar in the figure? ____________and ____________
2.) Write a proportion that shows the relation between the corresponding segments in the
triangles.
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Examples
1.) A 6-foot tall man, casting a 2-foot long shadow, is looking up at a building that casts a 22-foot long
shadow. Use the figure below to help calculate the height of the building.
1. Which segment represents the height of the building? ____________
2. On the figure to the right, label the segments that represent the height of the man and the
shadows with their lengths.
3. What triangles are similar in the figure? ____________and ____________
4. Write a proportion that shows the relation between the corresponding segments in the triangles.
Use it to find the height of the building:
2.) To find the distance d across the gorge, a student identifies points as shown in the figure. Find d.
3.) Architects draw buildings to scale in blueprints. A room in a new home will be 4.5 meters long and
3.3 meters wide. If the scale of the blueprint is 1 cm = 2.5 m, what should the dimensions be in the scale
drawing?
4.) Find the value of the height, h m, in the following diagram at which the tennis ball must be hit so that
it will just pass over the net and land 6 meters away from the base of the net.
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Independent Practice
1.) In a photo, Trish was standing near a cactus
on a sunny afternoon. She is 5.5 ft tall and her
shadow is 4 ft. Her classmates want to know the
height of the cactus that has a shadow of 9 ft.
What is the approximate height of the cactus?
2.) Benjamin is using a map to figure the
distance between two cities. The map scale
shows that 1 inch = 21 actual miles. If Benjamin
measures 9 inches between the two cities on
the map, what is the actual distance between
the two cities?
Lesson 28
4.) Esther built two similar rectangular tables.
The length of one of the tables is 8 feet and the
width is 4 feet. If the length of the second table
is 6 feet, what is its width?
5.) Two pieces of cloth are shaped like similar
triangles. The lengths of the sides of the first
piece of cloth are 5 inches, 9 inches, and 12
inches. The length of the shortest side of the
second piece of cloth is 15 inches. What is the
length of the longest side of the second piece of
cloth?
6.) To measure d, the distance across a lake,
Jeremy constructed similar, right triangles as
shown in the diagram. What is the distance, in
yards, across the lake?
3.) Derek sees that a 24 foot flagpole casts a 10
foot shadow. At the same time of day, if a
nearby tree casts a 25 foot shadow, about how
tall is the tree?
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