Similar and Congruent Triangles

ACT Math · Axiom Academy

LESSON Similar and Congruent Triangles Same shape, same size, or just the same proportions — and how the ACT turns that difference into fast points. 1. Congruent, Similar, and the Scale Factor Congruent triangles have the exact same shape AND size — every side and every angle matches (a photocopy). Similar triangles have the same shape but possibly different sizes — all angles match and all sides are proportional (an enlarged photo). Corresponding angles are equal Corresponding sides share one scale factor k 2. Proving Similarity: AA Is King To prove two triangles are similar you need just one of three conditions. Watch the star ACT setup: a line parallel to one side slides down , carving out a smaller triangle that is always similar to the whole. Two pairs of corresponding angles are equal. Since angles sum to 180° , the third follows for free. Two pairs of sides are proportional AND the included angle between them is equal. All three pairs of corresponding sides are proportional (same scale factor). Parallel lines cut by a transversal, a line parallel to one side of a triangle, or two right triangles sharing an acute angle. Worked example — parallel line inside a triangle In , with D on , E on . If AD = 3 , DB = 5 , and BC = 12 , then the scale factor is , so gives . 3. Matching Sides and Solving Proportions

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