Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional. :
Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional. AB = AC = BC DE DF EF A B C D E F
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If a line is parallel to one side of a triangle and intersects the other two sides in two distinct points, then it separates these sides into segments of proportional length. BD ║AE C A B D E 1 2 4 3
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If BE = 6, EA = 4, and BD = 9, find DC. 6x = 36 x = 6 Solve for x. 4x + 3 9 A B C D E 2x + 3 5 A B C D E
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If three or more parallel lines two transversals, they cut off the transversals proportionally. B A C D E F
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An angle bisector in a triangle separates the opposite side into segments that have the same ratio as the other two sides. CD is the bisector of ACB. A B C D
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If two triangles are similar, then the perimeters are proportional to the measures of the corresponding sides . Given: Δ ABC ~ Δ DEF, AB = 15, AC = 20, BC = 25, and DF = 4. Find the perimeter of Δ DEF. The perimeter of Δ ABC is 15 + 20 + 25 = 60. Side DF corresponds to side AC, so we can set up a proportion as follows: Perimeter of triangle ABC Side AC Side DF Perimeter of triangle DEF A B C D E F