Definition: Similar figures have the same shape but not necessarily the same size, with equal corresponding angles and proportional corresponding sides.
What does similar mean?
Two figures are similar when one is a scaled copy of the other. Angles match, and the ratios of matching sides are all equal.
How do you test it?
Compute the ratios. Triangle A has sides 6, 9, 12 and triangle B has sides 8, 12, 16. Ratios: 8/6, 12/9, and 16/12 all equal 4/3. So the triangles are similar with scale factor 4/3.
How do you find a missing side?
Set up a proportion. In similar triangles, a side of 15 corresponds to a side of 9, and another side of 20 corresponds to x. Then 15/9 = 20/x, so 15x = 180 and x = 12.
What is the transformation view?
Similar figures are related by a dilation plus rigid motions.
Where is it used?
Mathbot measures a tree’s height by comparing shadows. A 2 meter pole casts a 3 meter shadow, while the tree casts 21 meters. The tree is 2 x 21 / 3 = 14 meters tall.
What is a common mistake?
Comparing sides that do not correspond, or thinking equal ratio of just two sides is enough without checking all.