SAT and ACT math terms · SAT Math, ACT Math
Similar triangles
Similar triangles: Triangles with the same shape: corresponding angles are equal and corresponding sides are proportional.
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What it means
Two triangles are similar if two pairs of corresponding angles are equal (AA similarity). If the scale factor between similar figures is k, their areas have ratio k² and their volumes (for similar solids) have ratio k³.
Similar triangles often appear when a line parallel to one side cuts across a triangle.
Example
A 6-foot person casts a 4-foot shadow while a tree casts a 20-foot shadow. By similar triangles, the tree is 6/4 × 20 = 30 feet tall.
On the exam
Similarity appears in SAT geometry questions on lines, angles and triangles and in ACT triangles and similarity questions.