wunder beta🔍 Similar Shapes and Scale Factors
Similar shapes share the same shape but come in different sizes. Learn how the scale factor links them and use it to find missing lengths on maps, models, and enlargements.
What you’ll learn
- What Makes Shapes SimilarDefine similar shapes and test for similarity using angles and side ratios.Similar shapes are the same shape but different sizes, with one a scaled copy of the other. Two conditions define similarity: every pair of corresponding angles is equal, and every pair of corresponding sides is in the same ratio. Congruent shapes are a special case that are also the same size. If sides scale by different amounts, the shape is distorted and no longer similar.
- Using Scale FactorsFind and apply scale factors to calculate missing lengths in similar shapes.The scale factor is how many times bigger a similar copy is, found by dividing a new length by its matching original. Once known, multiply original lengths by it to find missing sides, or divide to reduce. Maps, model kits, and blueprints all use fixed scale factors so shapes stay in true proportion, such as a 1:100000 map where 1 cm represents 1 km.
Questions this course answers
Two shapes are similar when they have...
Similar shapes keep the same shape but differ in size — one is a scaled copy of the other.
In similar shapes, what is true about the corresponding angles?
Corresponding angles are equal in similar shapes; it is the side lengths that scale.
A photo is stretched taller but kept the same width. Is the new photo similar to the original?
Similarity needs all sides scaled by the same factor. Stretching only the height changes the proportions, so it is not similar.
How do you find the scale factor between two similar shapes?
The scale factor is a new length divided by its corresponding original length.
Two similar rectangles have widths 4 cm and 12 cm. If the small one is 5 cm tall, how tall is the large one?
The scale factor is 12 ÷ 4 = 3, so the height is 5 × 3 = 15 cm.
On a 1:100000 map, 1 cm represents how much real distance?
1 cm on the map equals 100000 cm of real land, and 100000 cm is 1 km.
Grounded in trusted sources
- Khan Academy — similarity and scale
- National Council of Teachers of Mathematics
- BBC Bitesize — similar shapes
- Britannica — similarity (geometry)
Every Wunder lesson is built from real, reputable sources — never invented.
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