Geometry & Trigonometry Medium
⏱ 15 min 📊 Medium ⭐ Premium

Similar and Congruent Triangles

Use similarity and congruence to find missing sides and angles in triangles.

Theory

Similar Triangles

Similar triangles (sim): Same shape, possibly different sizes. - All corresponding angles are equal - All corresponding sides are proportional: frac{a_1}{a_2} = frac{b_1}{b_2} = frac{c_1}{c_2} = k (scale factor) Tests for similarity: AA (two angles equal), SSS (all sides proportional), SAS (two sides proportional + included angle equal) Congruent triangles (cong): Same shape AND same size (k = …

Example: Triangle ABC sim DEF. If AB = 6, DE = 9, and BC = 8, find EF.

Summary

SAT Pro Tip

On the SAT, similar triangles often appear when: (1) two triangles share an angle and have parallel sides, (2) a line parallel to one side of a triangle divides the other two sides proportionally, or (3) right triangles share an angle.

similaritycongruencesat-geometry-trig

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