📚 Practice With Worksheets
Practice finding scale factor, comparing similar figures, and using proportional reasoning to understand enlargements, reductions, and missing side lengths.
▶️ Learn With Videos
Review how to find scale factors, use scale factors to calculate missing lengths, and solve scale drawing problems.
🛠️ How to Use This Tool
Click New Problem to generate two similar figures with a random direction, such as Figure A to Figure B or Figure B to Figure A.
Use the labeled corresponding sides to determine the scale factor, then enter your answer as a fraction or decimal.
Use Show Corresponding Sides for color-coded support, or click Reveal Work to review the scale factor setup.
🧠 Things to Notice
The scale factor depends on the direction of the comparison: new figure divided by original figure.
A scale factor greater than 1 creates an enlargement, while a scale factor less than 1 creates a reduction.
When the direction reverses, the scale factors are reciprocals of each other.
📘 Vocabulary
Scale Factor: The multiplier used to compare corresponding side lengths in similar figures.
Similar Figures: Figures that have the same shape but may have different sizes.
Corresponding Sides: Sides that match each other in similar figures based on position.
Enlargement: A copy of a figure that is larger than the original because the scale factor is greater than 1.
Reduction: A copy of a figure that is smaller than the original because the scale factor is less than 1.
Congruent Figures: Figures that have the same shape and same size; the scale factor is 1.
Reciprocal: A number formed by switching the numerator and denominator of a fraction.
Proportional: Having equivalent ratios or side lengths that are related by the same multiplier.
📐 Scale Factor Rules
To find a scale factor, divide a side length from the new figure by the corresponding side length from the original figure.
\(\text{Scale Factor}=\frac{\text{new length}}{\text{original length}}\)
Scale factors describe whether a figure is enlarged, reduced, or remains congruent.
\(k>1\text{ enlargement},\quad k<1\text{ reduction},\quad k=1\text{ congruent}\)
When comparing in the opposite direction, the scale factor becomes the reciprocal.
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