Quadrilaterals

• Parallelogram Opposite Sides Theorem says if a quadrilateral is a parallelogram, its opposite sides are congruent

  
• Parallelogram Opposite Sides Theorem Converse says if both pairs of opposite sides of a quadrilateral are congruent, it's a parallelogram

  
• Parallelogram Opposite Angles Theorem says if a quadrilateral is a parallelogram, its opposite angles are congruent

  
• Parallelogram Opposite Angles Theorem Converse says if both pairs of opposite angles of a quadrilateral are congruent, its a parallelogram
• Consecutive Angles of a Parallelogram Theorem says a parallelogram has consecutive angles
• Consecutive Angles of a Parallelogram Theorem Converse says if consecutive angles of a quadrilateral are supplementary, its a parallelogram
• Parallelogram Diagonals Theorem says if a quadrilateral is a parallelogram, its diagonals bisect each others
• Parallelogram Diagonals Theorem Converse says if diagonals of a quadrilateral bisect each other, its a parallelogram
• One Pair Congruent and Parallel Sides Theorem says if one pair of opposite sides of a quadrilateral are congruent and parallel, its a parallelogram
• A rhombus is a parallelogram with 4 congruent sides; has diagonals that are perpendicular; diagonals bisect opposite angles
• A square is a parallelogram with 4 congruent sides and 4 right angles; the diagonals are perpendicular + bisect opposite angles
• A rectangle is a parallelogram with 4 right angles; the diagonals are congruent
• The Rhombus Corollary says a quadrilateral is a rhombus if it has 4 congruent sides
• The Rectangle Corollary says a quadrilateral is a rectangle if it has 4 right angles
• Square Corollary says a quadrilateral is a square if it is a rhombus and a rectangle
• Rhombus Diagonals Theorem says a parallelogram is a rhombus if its diagonals are perpendicular
• Rhombus Diagonals Theorem Converse says if the diagonals of a parallelogram are perpendicular, its a rhombus
• Rectangle Diagonals Theorem says a parallelogram is a rectangle if its diagonals are congruent
• Rectangle Diagonals Theorem Converse says if the diagonals of a parallelogram are congruent, its a rectangle
• A trapezoid is a quadrilateral with at least 1 pair of parallel sides; it has 2 pairs of base angles
• An isosceles trapezoid has congruent legs; its diagonals are congruent; its base angle pairs are congruent

  
• Trapezoid Diagonals Theorem says if a trapezoid is isosceles, its diagonals are congruent
• Trapezoid Diagonals Theorem Converse says if a trapezoid has congruent diagonals, its isosceles
• Isosceles Trapezoid Theorem says an isosceles trapezoid has congruent pairs of base angles
• Isosceles Trapezoid Theorem Converse says if a trapezoid has a pair of congruent base angles, its isosceles
• Trapezoid Midsegment Theorem says the midsegment of a trapezoid is parallel to its base; the length is 1/2 sum of length of bases

  
• A kite is a quadrilateral with 2 pairs of congruent sides; its opposite sides are not congruent; one diagonal bisects opposite angles
• Kite Diagonals Theorem says a kite's diagonals are perpendicular
• A parallelogram is a quadrilateral with two pairs of parallel sides