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# Chapter 8 Notecards

TermDefinition
Diagonal diagonal of a polygon is a segment that joins two nonconsecutive vertices
Polygon Interior Angles Theorem The sum of the measures of the interior angles of a convex n-gon is (n-2)180
Interior Angles of a Quadrilateral Corollary The sum of the measures of the interior angles of a quadrilateral is 360
Polygon Exterior Angles Theorem The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360.
Parallelogram a quadrilateral with both pairs of opposite sides parallel.
Theorem 8.3 if a quadrilateral is a parallelogram then its opposite sides are congruent
Theorem 8.4 if a quadrilateral is a parallelogram then its opposite angles are congruent
Theorem 8.5 if a quadrilateral is a parallelogram then its consecutive angles are supplementary
Theorem 8.6 if a quadrilateral is a parallelogram then its diagonals bisect each other
Theorem 8.7 if both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram
Theorem 8.8 if both pairs of opposite angles of a quadrilateral are congruent then the quadrilateral is a parallelogram
Theorem 8.9 if one pair of opposite sides of a quadrilateral are congruent and parallel then the quadrilateral is a parallelogram
Theorem 8.10 if the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram
Rhombus a parallelogram with four congruent sides
Rectangle a parallelogram with four right angles
Square a parallelogram with four congruent sides and four right angles.
Rhombus Corollary a quadrilateral is a rhombus if and only if it has four congruent sides
Rectangle Corollary a quadrilateral is a rectangle if and only if it has four right angles
Square Corollary a quadrilateral is a square if and only if it is a rhombus and a rectangle
Theorem 8.11 a parallelogram is a rhombus if and only if its diagonals are perpendicular
Theorem 8.12 a parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles
Theorem 8.13 a parallelogram is a rectangle if and only if its diagonals are congruent
Trapezoid a quadrilateral with exactly one pair of parallel sides
Bases of a Trapezoid The parallel sides are the bases and there is only two pairs of base angles.
Legs of a Trapezoid the nonparallel sides
Theorem 8.14 if a trapezoid is isosceles then each pair of base angles is congruent
Theorem 8.15 if a trapezoid has a pair of congruent base angles then it is an isosceles trapezoid
Theorem 8.16 a trapezoid is isosceles if and only if its diagonals are congruent
Midsegment of a Trapezoid the segment that connects the midpoints of its legs
Midsegment Theorem for Trapezoids the midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases
Kite a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent
Theorem 8.18 if a quadrilateral is a kite then its diagonals are perpendicular
Theorem 8.19 if a quadrilateral is a kite then exactly one pair of opposite angles are congruent