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Similarity and Scale Factors
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Similarity and Scale Factors
📐 Part 1: Understanding Similarity
1. Two triangles are similar if they have the same _______ but different _______.
2. If triangle ABC is similar to triangle DEF with a scale factor of 3, and side AB = 4 inches, what is the length of corresponding side DE?
7 inches
12 inches
1.33 inches
4 inches
3. When shapes are similar, which properties are preserved? (Check all that apply)
Angle measures
Side length ratios
Actual side lengths
Shape
4. A rectangle has dimensions 6 ft by 9 ft. If it's scaled by a factor of 1/3, what are the new dimensions?
New length: _______ ft New width: _______ ft
📊 Part 2: Coordinate Plane Dilations
5. The algebraic rule for dilation centered at the origin is (x, y) → (____, ____) where k is the scale factor.
6. Point A is at (2, 4). After a dilation with scale factor 2.5 centered at the origin, what are the coordinates of A'?
7. Triangle PQR has vertices P(1, 2), Q(3, 2), and R(2, 4). If the triangle is dilated by a scale factor of 3, find the coordinates of the image triangle P'Q'R'.
8. A square has vertices at (0, 0), (2, 0), (2, 2), and (0, 2). After dilation with scale factor 0.5, what is the perimeter of the new square?
4 units
8 units
2 units
16 units
🏠 Part 3: Real-World Applications
9. An architect creates a scale drawing of a house where 1 inch = 8 feet. If a room measures 2.5 inches by 3 inches on the drawing, what are the actual dimensions of the room?
10. Explain in your own words: How does understanding scale factors help when working with maps, blueprints, or models? Give a specific example.
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