Similar Figures
Similar figures are shapes with the same form but different sizes in Grade 8 math (Yoshiwara Core Math). They have equal corresponding angles and proportional corresponding sides — the ratio of any two corresponding sides equals the scale factor. Triangles with sides 3,4,5 and 6,8,10 are similar (scale factor 2). Similar figures appear in photography, maps, and architecture. Finding missing sides requires setting up and solving proportions between corresponding sides.
Key Concepts
Property Two figures are similar if, and only if: 1. Their corresponding angles are equal, and 2. Their corresponding sides are proportional.
Examples A rectangle with sides 4 cm and 6 cm is similar to a rectangle with sides 8 cm and 12 cm. The scale factor is 2.
A photograph measuring 4 inches by 6 inches is enlarged to 8 inches by 12 inches. The enlarged photo is similar to the original.
Common Questions
What makes two figures similar?
Corresponding angles are equal AND corresponding sides are proportional.
What is the scale factor between similar figures?
The ratio of corresponding sides. E.g., 3,4,5 triangle and 6,8,10 triangle: scale factor = 2.
How do you find a missing side in similar figures?
Set up a proportion: 3/6 = x/8 → x = 4.
Are all squares similar to each other?
Yes. All squares have 90° angles and equal sides — any two squares have equal angles and proportional sides.
How is similarity different from congruence?
Congruent figures are identical in size and shape. Similar figures have the same shape but different sizes.