Day 6 and 7 - Angle Inequalities

Definition of Inequality - for any real numbers a and b, a > b if and only if there is a positive number c such that a = b + c

Exterior Angle Inequality Theorem - if an angle is an exterior angle of a triangle, then its measure is greater than the measure of either of its corresponding remote interior angles

Theorem - if one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side

Theorem - If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle

Theorem - The perpendicular segment from a point to a line is the shortest segmennt from the point to that line

Triangle Inequality Theorem - the sum of the lengths of any two sides of a triangle is greater than the lengths of the third side

SAS Inequality Theorem - if two sides of one triangle are congruent to two sides of another triangle and the included angle in one triangle has a greater measure than the included angle in the other, then the third side of the first triangle is longer than the third side of the second triangle

SSS Inequality Theorem - if two sides of one triangle are congruent to two sides of another triangle and the third side in one triangle is longer than the third side in the other, then the angle between the pair of congruent sides in the first triangle is greater than the corresponding angle un the second triangle

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