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# Algebra 5.7-5.12

Theorem 5.18 If a quadrilateral is a paralellogram, then its opposite sides are congruent
Theorem 5.19 If a quadrilateral is a paralellogram, then its opposite angles are congruent
Theorem 5.20 If a quadrilateral is a paralellogram, then its consecutive angles are supplementary
Theorem 5.21 If a quadrilateral is a parallelogram, then its diagonals bisect eachother
Theorem 5.22 If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a paralellogram
Theorem 5.23 If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a paralellogram
Theorem 5.24 If on pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram
Theorem 5.25 If the diagonals of a quadrilateral bisect eachother, then the quadrilateral is a paralellogram
Theorem 5.26 A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles
Theorem 5.27 A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles
Theorem 5.28 A parallelogram is a rectangle if and only if its diagonals are congruent
Theorem 5.29 If a trapezoid is isosceles, then each pair of base angles is congruent
Theorem 5.30 If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid
Theorem 5.31 A trapezoid is isosceles if and only if its diagonals are congruent
Theorem 5.32 (Midsegment Theorem for Trapezoids) the midesegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the base
Theorem 5.33 If a quadrilateral is a kite, then its diagonals are perpendicular
Theorem 5.34 If a quadrilateral is a kite, then exactly one pair of opposite sides is congruent
Created by: eunbyul