📚 Practice With Worksheets
Practice drawing scaled figures, finding scale factors, and using proportions to compare similar figures.
▶️ Learn With Videos
Review how to identify similar figures, calculate scale factors, and express scale factors in different forms.
🛠️ How to Use This Tool
Choose a starter figure, then drag Shape 1 or its blue handles to move and reshape the original figure.
Use the scale factor slider to enlarge or reduce Shape 2, and use the rotation slider to turn it while preserving similarity.
Pan the graph by dragging empty space, zoom with the mouse wheel or pinch gesture, and use Reset View or Fit Figures whenever you want to recenter the display.
🧠 Things to Notice
As the scale factor changes, every corresponding side length is multiplied by the same number.
Rotating or moving a figure changes its position or orientation, but it does not change the proportional relationship between corresponding sides.
Corresponding angles remain congruent while corresponding side lengths remain proportional, which is what makes the figures similar.
📘 Vocabulary
Similar Figures: Figures that have the same shape, with congruent corresponding angles and proportional corresponding side lengths.
Scale Factor: The number multiplied by each side length of the original figure to produce the corresponding side length in the image.
Corresponding Sides: Sides that occupy matching positions in two similar figures.
Corresponding Angles: Angles that occupy matching positions in two similar figures and have equal measures.
Proportional: Having equal ratios between corresponding quantities.
📐 What to Pay Attention to With Similar Figures
A scale factor describes multiplication. To move from an original side length to its corresponding image side length, multiply by the scale factor.
Image length = Original length × Scale factor
The size of the scale factor tells what kind of change occurred: a factor greater than 1 is an enlargement, a factor between 0 and 1 is a reduction, and a factor of exactly 1 produces congruent figures.
k > 1: enlargement 0 < k < 1: reduction k = 1: congruent
Reversing the direction of comparison uses the reciprocal scale factor. For example, if the scale factor from Shape 1 to Shape 2 is 3/2, then the scale factor from Shape 2 back to Shape 1 is 2/3.
Reverse scale factor = 1 ÷ Original scale factor
Corresponding angles stay congruent, while corresponding side lengths stay proportional. Moving or rotating a figure does not change whether the figures are similar.
🔗 Share This Math Tool
Found this resource helpful? Share it with another teacher or save the link for later.
🚀 Explore More Math Tools
Browse more interactive tools for probability, statistics, algebra, geometry, ratios, and number systems.
Explore More Math Tools