Similarity

• Equivalent ratios are ratios with the same simplified form
• A proportion is an equation that shows two ratios are equal (a/b=c/d)
• Extremes are values of proportion that are furthest apart in ratios (a and d)
• Means are values of proportions that are the middle terms in ratio (b and c)
• A geometric mean of two positive numbers is a/x = x/b, x^2 = ab
• The Reciprocal Property is two equal ratios have equal reciprocals
• True proportions are a/b = c/d (original); a/c = b/d (means switch); a+b/b = c+d/d (add value of ratio denominator)
• Similar polygons have congruent corresponding angles and corresponding side lengths that are proportional
• A scale factor is a ratio between shapes; you read the similarity statement to see how the fraction is written
• The perimeter ratios of two similar polygons equals the ratio of their side lengths
• Angle Angle Similarity Postulate says if two angles are congruent to two angles of another triangle, they are similar
• Side Side Side Similarity Theorem says two triangles are similar if their corresponding side lengths are proportional
• The Triangle Proportionality Theorem says if a line parallel to one side of a triangle intersects the other two sides; the two sides are divided proportionally

  
• Triangle Proportionality Theorem Converse if a line divides two sides of a triangle proportionally, its parallel to the 3rd side

  
• Angle Bisector Theorem says if a ray bisects an angle of a triangle, it divides the opposite sides into segments with lengths proportional to the other two sides

  
• CASTC is corresponding angles of similar triangles are congruent
• CSSTP is corresponding sides of similar triangles are proportional
• Side Angle Side Similarity Theorem says if a triangle angle is congruent to another triangle angle, and the side lengths and angles are proportional, the triangles are similar

  
• Three Parallel Lines Theorem says if 3 parallel lines intersect 2 transversals, then divide the transversals proportionally

  
• The Right Triangle Similarity Theorem says an altitude that is drawn to the hypotenuse of a right triangle makes the 2 triangles formed similar to the original triangle and others

  
• An area ratio is found by squaring the scale factor; a scale factor is found by taking the square root of the area ratio