Scaled Copies & Corresponding Parts
What is true about all corresponding angles in a figure and its scaled copy?
They are always equal
A scale factor that produces a scaled copy LARGER than the original figure must be in this numerical range
Greater than 1
On a map, the scale is 1 inch = 5 miles. If two cities are 4 inches apart on the map, what is the actual distance between them?
20 miles
If you scale a figure using a scale factor of 3, the area of the new figure is multiplied by this number.
9 (32)
A triangle has side lengths of 3 cm, 4 cm, and 5 cm. A student draws a copy with side lengths of 6 cm, 7 cm, and 8 cm. Explain why this is NOT a scaled copy.
The side lengths were increased by adding 3 instead of multiplying by a scale factor
A scale factor that produces a scaled copy SMALLER than the original figure must be in this numerical range.
Between 0 and 1
A floor plan uses a scale of 1 cm = 2 meters. If an actual bedroom is 6 meters long, how long will it be on the drawing?
True or False: If you scale a polygon using a scale factor of K, the perimeter is multiplied by K, but the area is multiplied by K2
True
If Segment AB corresponds to Segment JK, and Segment AB = 6 units while Segment JK = 18 units, what is the scale factor?
An original line segment measures 12 cm. Its scaled copy measures 3 cm. What is the scale factor from the original to the copy?
1/4
A map has a scale of 2 cm = 15 km. If the distance between two parks on the map is 7 cm what is the actual distance
52.5 km
An original shape has an area of 15 square units. A student creates a scaled copy using a scale factor of 3. What is the area of the scaled copy?
135 units2
original area x SF2
15 x 32 = 15 x 9 = 135 units2
This is the reciprocal operation or fraction needed to take a scaled copy with a scale factor of 4 back to its original size.
multiplying by 1/4
If the scale factor from Figure A to Figure B is 2/5, what is the scale factor from Figure B back to Figure A?
5/2 or 2.5
You have a drawing with a scale of 1 in = 10 ft. You recreate the drawing using a new scale of 1 in = 5 ft Will the new drawing be LARGER or SMALLER than the first drawing? How much LARGER or SMALLER will it be?
Rectangle A is 8 inches by 2 inches. Rectangle B is a scaled copy of Rectangle A. Which of these dimensions could be Rectangle B?
A. 10 in by 2.5 in
B. 9 in by 3 in
C. 40 in by 10 in
A. SF = 1.25
C SF = 5
Name two specific characteristics that MUST be true for a figure to be considered a scaled copy of another figure.
All corresponding angles are equal, and (2) All corresponding distances are multiplied by the same scale factor
Rectangle A measures 4 cm by 10 cm. Rectangle B measures 6 cm by 15 cm. What is the scale factor from A to B?
3/2 or 1.5
Lin made a scale drawing of a rectangular playground using the scale 1 cm = 6 meters. Her drawing is 5 cm long and 3 cm wide.
Diego creates a new scale drawing of the same playground using a scale of 1 cm = 2 meters. What are the dimensions (length and width) of Diego's drawing.
15 cm long and 9 cm wide
1. Find actual size
Actual Length = 5 cm x 6 m = 30
Actual width = 3 cm x 6 m = 18 m
2. Convert to Diego's scale
Diego's length = 30 m / 2cm = 15 cm
Diego's width = 18 m / 2 cm = 9 cm
A scale drawing of a rectangular parking lot is 6 inches long and 5 inches wide. The actual parking lot is 240 feet long. What is the area of the actual parking lot in square feet?
48,000 ft2
Scale: 6 in = 240 ft --> 1 in = 40 ft
Actual width: 5 x 40 = 200
Actual Area: 240 x 200 = 48,000 ft2