Transcript Similar Shapes and Scale Drawings

Similar Shapes and Scale
Drawings
Warm Up
• A scale drawing is proportional to a life size
drawing of the same object.
• A scale is a ratio between two sets of
measurements and is usually shown as two
numbers separated by a colon.
• Scale drawing problems are solved using
proportional reasoning and finding equivalent
ratios.
• Changing the scale of a drawing to a new scale
with larger numbers will decrease the size of
the drawing, not increase it.
• Scale drawings have many applications in
everyday life.
Charlie and Zachery are each
making a scale drawing of the
school garden. The garden
measures 30 feet by 12 feet.
Charlie plans to use a scale of
1 inch: 2 feet. Zachery plans to use
a scale of 2 inches: 1 foot.
Which is the better plan?
Justify your answer.
• You use scale drawings to represent
measurements of actual objects or places.
• You can find dimensions of actual objects by
making and completing a table or by writing
and solving proportions.
• A scale drawing must be proportional to a lifesize drawing of the same object.
• Since a scale drawing and a life-size drawing
are proportional, they are similar: any
corresponding angles will have equivalent
measures, and the ratios of the lengths of
corresponding sides are proportional.
Are the scales 2 in.:3 ft. and 1:18
the same scale? Explain.
Can you multiply the numerator
2 𝑖𝑛.
and denominator of
3 𝑓𝑡.
by the same number to show
2 𝑖𝑛.
11 𝑖𝑛.
=
? Explain.
3 𝑓𝑡.
16.5 𝑓𝑡.
How can you use a scale to determine whether
the drawing or the object is larger?
• Put both parts of the scale in the same
unit.
• If the first number is greater, then the
drawing is larger.
• If the second number is greater, then the
object is larger.
Joanne has a scale drawing of her
backyard that includes a garden
bed that measures 25 inches long
and 16 inches wide. What is the
area of the actual garden bed?
How do you use the scale on a scale
drawing to find the measurements of
the actual object?
• Write the scale as a ratio in fraction
form.
• Use the ratio to write a proportion that
uses measurements from the scale
drawing.
• Use proportional reasoning to solve for
the actual measurements in the
proportion.
The scale in the drawing is
2 in.:4 ft. What are the length and
width of the actual room? Find the
area of the actual room.
The scale in the drawing is
2 cm:5 m. What are the length and
width of the actual room? Find the
area of the actual room.
The area of a square floor on a
scale drawing is 100 square
centimeters, and the scale of the
drawing is 1 cm:2 ft. What is the
area of the actual floor? What is
the ratio of the area in the drawing
to the actual area?
A billboard is 2.5 times as long as it
is wide. The area of the billboard is
2
2,250 𝑓𝑡 . A scale drawing is made
of the billboard, and the area of
2
the scale drawing is 160 𝑖𝑛 . What
is the scale used in the scale
drawing? Explain.
Exit Ticket
1. A scale drawing of a billboard uses the scale 4 cm:9 ft.
The length of the billboard in the drawing is 11 cm.
How long is the actual billboard?
2. A scale drawing of a dance
floor is shown. What is the area
of the actual dance floor?
3. A bookcase measures 13 feet wide and 24 feet tall.
What would the bookcase’s measurements be on a
scale drawing using the scale 3 cm:2 ft?
4. Bob makes a scale drawing of a statue using the scale
1cm:5 ft. His drawing measures 12 cm. Kia makes a
scale drawing of the same statue using the scale
1cm:4 ft. How many centimeters tall is the statue in
Kia’s drawing?