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# math ch. 8 theorems

### math ch 8 vocab... postulates... theorems

polygon interior Angles Theorem the sum of the measures of the interior angles of a convex n-gon is (n-2)*180 degrees
corollary the sum of the measures of the interior angles of a quadrilateral is 180 degrees.
polygon Exterior Angles Theorem the sum of the measures of the exterior angles if a convex polygon, one angle at each vertex, is 360 degrees
polygon Exterior Angles Theorem 2 if a quadrilateral is a parallelogram, then its opposite sides are congruent.
polygon Exterior Angles Theorem 3 if a quadrilateral is a parallelogram, then its opposite angles are congruent
polygon Exterior Angles Theorem 4 if a quadrilateral is a parallelogram, then its diagonals bisect each other
polygon Exterior Angles Theorem 5 if both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram,.
polygon Exterior Angles Theorem 6 if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
polygon Exterior Angles Theorem 7 if one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram
polygon Exterior Angles Theorem 8 of the diagonals of a quadrilateral bisect each of other then the quadrilateral is a parallelogram.
polygon Exterior Angles Theorem 9 if one pair of opposite sides are congruent and parallel then the quadrilateral is a parallelogram.
Rhombus corollary a quadrilateral is a rhombus if and only if if has four congruent sides.
Rectangle corollary a quadrilateral is a rectangle if and only if if has four right angles.
square corollary a quadrilateral is a square is and only if its a rhombus and a rectangle.
shapes corollary a parallelogram is a rhombus if and only if its diagonals are perpendicular.
shapes corollary 2 a parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.
shapes corollary 4 a parallelogram is a rectangles if and only if its diagonals are congruent.
shapes corollary 5 if a trapezoid is isosceles, then both pairs of base angles are congruent.
shapes corollary 6 if a trapezoid has a pair of congruent base angles, them it is an isosceles trapezoid.
shapes corollary 7 a trapezoid is isosceles if and only is its diagonals are congruent.
Midsegment Theorem for trapezoids the mud segment of a trapezoid is parallel to each bas and its length if one half the sum of the lengths of the bases.
Midsegment Theorem for trapezoids 2 if a quadrilateral is a kite, then exactly on pair of opposite angles are congruent.
Midsegment Theorem for trapezoids 3 if a quadrilateral is a kite then its diagonals are perpendicular.
Created by: the cat