Triangle Similarity

Geometry · Axiom Academy

Same shape, different size — understanding proportional triangles. Two triangles are similar (written ) when every corresponding angle is equal and every corresponding side scales by the same factor. Watch a triangle grow: the angles never move, and all three sides stretch by the same scale factor k at once. corresponding angles equal AND corresponding sides proportional 2. Three Ways to Prove Similarity You don't need to check everything. Any one of these three conditions is enough to guarantee two triangles are similar. The animation shows each test in turn. If two angles of one triangle equal two angles of another, the triangles are similar. If all three pairs of corresponding sides are proportional , the triangles are similar. If two sides are proportional and the included angle is equal , the triangles are similar. When triangles are similar, corresponding sides are proportional: Once you know two triangles are similar, the scale factor turns every known side into its match. The sweep below scales each side of by k to build . . If AB = 6 , BC = 8 , AC = 10 , and DE = 9 , find EF and DF . Every congruent pair is also similar — with scale factor k = 1 . You've seen what makes triangles similar, the three ways to prove it, and how the scale factor unlocks every missing side. Scroll up to revisit any step.

This is the written version of the interactive lesson above. See the full Geometry course.