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Similarity and Scale Factors
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Similarity and Scale Factors
📐 Part 1: Understanding Similarity and Scale Factor
1. Two triangles are similar. The sides of the first triangle are 3 inches, 4 inches, and 5 inches. If the scale factor is 2, what are the side lengths of the second triangle?
6 inches, 8 inches, 10 inches
5 inches, 6 inches, 7 inches
1.5 inches, 2 inches, 2.5 inches
9 inches, 16 inches, 25 inches
2. A point (4, 6) is dilated by a scale factor of 3 centered at the origin. What are the new coordinates?
(7, 9)
(12, 18)
(1, 2)
(4, 6)
3. Which properties remain the same when a figure is dilated? Check all that apply:
Angle measures
Side lengths
Shape
Area
4. A scale factor of 0.5 will create a figure that is:
Larger than the original
Smaller than the original
The same size as the original
Upside down from the original
🏗️ Part 2: Real-World Applications
5. An architect creates a blueprint of a house using a scale factor of 1:48. If a room measures 2 inches on the blueprint, what is the actual length of the room in feet?
Show your work:
Answer: _______ feet
6. A toy car is a scale model of a real car with a scale factor of 1:32. If the real car is 16 feet long, how long is the toy car in inches?
Show your work:
Answer: _______ inches
7. Triangle ABC has vertices at A(2, 4), B(6, 2), and C(4, 8). If the triangle is dilated by a scale factor of 1.5 centered at the origin, find the coordinates of the new triangle A'B'C'.
A' = (_____, _____)
B' = (_____, _____)
C' = (_____, _____)
💭 Part 3: Critical Thinking
8. Explain in your own words what happens to the coordinates of a point when it is dilated by a scale factor of 4 centered at the origin.
9. A rectangle has dimensions 6 cm by 9 cm. After dilation, the new rectangle has dimensions 4 cm by 6 cm. What was the scale factor used?
Scale factor = _________
Explain how you found your answer:
10. Two similar polygons have a scale factor of 3:5. If the perimeter of the smaller polygon is 18 inches, what is the perimeter of the larger polygon?
Show your work:
Answer: _______ inches
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