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Postulates

Chapter 8 Quadrilaterals

Postulate/ TheoromDefinition
polygon interior angles theorom the sum of the measures of the interior angles of a convex n-gon is (n-2)X 180.
interior angles of a quad. thrm the sum of the measures of the interior angles of a quad is 360.
polygon exterior angles thrm. the sum of the measures of sthe exterior angles of a convex polygon, one angle at a vertex, is 360
8.3 if a quad is a parallelogram this its opp sides are congruent
8.4 if a quad is a parallelogram the its opp angles are congruent
8.5 if a quad us a parallelogram then its consecutive angles are supp
8.6 if a quad is a parallelogram then its diagonals bisect each other
8.7 if both pairs of opp sides of a quad are congruent then the quad is a parallelogram
8.8 if both pairs of opp angles of a quad are congruent then the quad is a parallelogram
8.9 if one pair of opp sides of a quad are congruent then the quad is a parallelogram
8.10 if the diagonals of a quad bisect each other the the quad is a parallelogram
rhombus corollary a quad is a rhombus if and only if it has four congruent sides
rectangle corollary a quad is a rectangle if and only if it has four right angles
square corollary a quad is a square if and only if its a rhombus and a rectgangle
8.11 a parallelogram us a rhombus if and only if its diagonals are perpendicular
8.12 a parallelogram is a rhombus if and only if each diagonal bisects a pair of opp angles
8.13 a parallelogram is a rectangle if and only if its diagonals are congruent
8.14 if a trapezoid is isosceles, then each pair of base angles are congruent
8.15 if a trapezoid has a pair of congruent base angles, then its an isosceles trapezoid
8.16 a trapezoid is isosceles if and only if its diagonals are congruent
8.17 the midsegment of a trapezoid is parallel to each base and its length is one half the sume of its bases
8.18 if a quad is a kite, then its diagonals are perpendicular
8.19 if a quad is a kite, then exactly one pair of opp angles ar congruent