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### 17 Cards in this Set

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 Triangle Inequality Theorem a. The third side of any triangle must be a measure in between the sum and the difference of the other two sides. b. In any triangle, the longest side is opposite the largest angle and the shortest side is opposite the smallest angle. c. The sum of any two sides of a triangle is greater than the third side. Locus all of the points that satisfy a given situation similar figures figures are congruent if and only if corresponding angles are congruent and corresponding sides are proportional ratio a comparison of two values proportion two equal ratios 4-in-1 theorem in similar triangles, the corresponding altitudes are in the same ratio as the corresponding SIDES, ANGLE BISECTORS, MEDIANS, AND PERIMETERS in a right triangle with an altitude drawn to the hypotenuse.... a. the three right triangles similar to eachother. b. the altitudes is the geometric mean of the two parts of the hypotenuse that it divides. c. the leg is the geometric mean of the hypotenuse and the part of the hypotenuse it is adjacent to. corilary theorems if a2 + b2 = c2 then the triangle is right. if a2 + b2 < c2 then the triangle is obtuse. if a2 + b2 > c2 then the triangle is acute. 2 = squared circumcenter FORMED BY: perpendicular bisectors RULE: equidistant to all 3 verticies of a triangle. incenter FORMED BY: angle bisectors RULE: equidistant to all 3 sides of a triangle. centroid FORMED BY: medians RULE: the length of the segment from the centroid to the vertex is 2 times the length of the segment from the centroid to the side orthocenter FORMED BY: altitudes RULE: cevas theorem central angle anangle whos vertex is at the center and its sides are both radii inscribed angle an angle whos vertex is on the circle and whos sides are chords interior angle an angle whos vertex is an interior point and the angle is formed by the intersection of 2 chords exterior angle an angle whos vertex is an exterior point and whos sides are either 2 secants, 2 tangents or a secant and a tangent in similar figures... in similar figures, the ratio of the areas = the square of the ratio of the corresponding sides.