Similar Shapes and Scale Factors
Two shapes are similar if they have the same shape but different sizes: all corresponding angles are equal and corresponding sides are in the same ratio. The ratio of corresponding sides is called the scale factor.
What You Need to Know
Key Concept Diagram
Similar shapes have equal corresponding angles and proportional corresponding sides
The scale factor is the ratio of a side in the image to the corresponding side in the original
If the scale factor is k, areas are multiplied by k^2
Congruent shapes are a special case of similarity where the scale factor equals 1
Scale drawings and maps use similarity: actual length = map length x scale factor
Key Vocabulary
Similar
Shapes that have the same angles and proportional sides but may be different in size
Scale Factor
The ratio by which all side lengths are multiplied when making a similar shape
Corresponding Sides
Sides in the same relative position in two similar figures
Congruent
Shapes that are exactly the same size and shape (scale factor = 1)
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Two triangles are similar. The sides of the smaller triangle are 3, 4, and 5 cm. The longest side of the larger triangle is 15 cm. What is the scale factor?
Question 2
A rectangle has dimensions 4 cm x 6 cm. A similar rectangle has a scale factor of 2.5. What is the area of the larger rectangle?
Question 3
A map has a scale of 1:50,000. A road that is 6 cm on the map is how long in real life?
Key Concepts Summary
- ●Similar shapes have equal corresponding angles and proportional corresponding sides
- ●The scale factor is the ratio of a side in the image to the corresponding side in the original
- ●If the scale factor is k, areas are multiplied by k^2
- ●Congruent shapes are a special case of similarity where the scale factor equals 1
- ●Scale drawings and maps use similarity: actual length = map length x scale factor