Similar and Congruent Triangles

SAT Math · Axiom Academy

Similar and Congruent Triangles When triangles are the same shape, their sides are proportional — the single idea behind a huge share of SAT geometry questions. The difference between congruent (same shape and size) and similar (same shape, scaled) The shortcuts that prove triangles congruent or similar How to set up a proportion to find a missing side Why the ratio of areas is the square of the ratio of sides Once triangles are similar, write corresponding sides as a proportion and solve. The order of the letters tells you which sides correspond. with AB = 6 , DE = 9 , and BC = 8 . Find EF . In , with D on AB and E on AC . If AD = 4 , DB = 6 , and AE = 5 , find EC . Two similar triangles have areas 16 and 49 . What is the ratio of their corresponding sides? Two similar triangles have areas in the ratio 9 : 25 . What is the ratio of their perimeters? Perimeter scales like the sides: So the perimeters are in the ratio 3 : 5. A 5 -ft pole casts a 3 -ft shadow. At the same moment, a flagpole casts a 24 -ft shadow. How tall is the flagpole? Congruent = same size; similar = same shape, scaled. AA is usually enough to prove similarity — then all corresponding sides share one ratio. A line parallel to a side of a triangle cuts off a similar triangle. Area ratio ; reverse it by taking a square root.

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