Similar shapes

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Last updated 7:51 PM on 7/28/26
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17 Terms

1
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What are similar shapes?
Shapes where one is an exact enlargement or reduction of the other.
2
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What is true about corresponding angles in similar shapes?
Corresponding angles are strictly equal (identical).
3
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What is true about corresponding sides in similar shapes?
Corresponding sides are in the same proportion (scaled by the same scale factor).
4
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What is the difference between congruent and similar shapes?
Congruent shapes have the exact same shape and size. Similar shapes have the same shape but different sizes.
5
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What is the definition of a scale factor (k)?
The number you multiply or divide by to convert side lengths between similar shapes.
6
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Formula: Length Scale Factor (k)
k = (Length on Enlarged Shape) ÷ (Corresponding Length on Original Shape)
7
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How do you find a missing length on a LARGER similar shape?
Multiply the corresponding smaller length by the scale factor (k).
8
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How do you find a missing length on a SMALLER similar shape?
Divide the corresponding larger length by the scale factor (k).
9
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What are the 3 steps to find a missing side length?
1. Find a known matching pair of corresponding sides. 2. Calculate k (larger ÷ smaller). 3. Multiply or divide by k.
10
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What are nested similar triangles?
A smaller triangle hidden inside a larger triangle, typically sharing an angle or parallel lines.
11
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How do you solve nested similar triangle problems?
1. Identify shared or parallel angles. 2. Redraw the two triangles separately. 3. Use total lengths for the larger triangle.
12
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What is the Area Scale Factor in terms of length scale factor (k)?
k² (Area increases by k squared).
13
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What is the Volume Scale Factor in terms of length scale factor (k)?
k³ (Volume increases by k cubed).
14
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If length scale factor k = 2, what are the Area and Volume scale factors?
Area scale factor = 4 (2²); Volume scale factor = 8 (2³).
15
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Formula: Calculating New Area
New Area = Original Area × k²
16
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Formula: Calculating New Volume
New Volume = Original Volume × k³
17
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Summary: 1D vs 2D vs 3D scale factors
Length = k, Area = k², Volume = k³