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Section 9-1
Properties of Parallelograms

Theorem 9-1: Opposite sides of a parallelogram are congruent

Theorem 9-2: Opposite angles of a parallelogram are congruent angles of a polygon that share a common side are consecutive angles (supplements)

Theorem 9-3: The diagonals of a parallelogram bisect each other (bisects the diagonal, itself, not the angle)

Theorem 9-4: If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal

Section 9-2

Proving that quadrilaterals are parallelograms

Theorem 9-5: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram

Theorem 9-6: If one pair of opposite sides of a quarilateral are both congruent and parallel, then the quadrilateral is a parallelogram

Theorem 9-7: if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram

Theorem 9-8: if both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram

Section 9-3
Properties of Special Parallelograms

Theorem 9-9: Each diagonal of a rhombus bisects two <'s of a rhombus

Theorem 9-10: The diagonals of a rhombus are perpendicular

Theorem 9-11: The area of a rhombus is equal to 1/2
The product of the lengths of its diagonals A=1/2 (d1)(d2)

Theorem 9-12: The diagonals of a rectangle are congruent

Theorem 9-13: If one diagonal of a parallelogram bisects 2<'s of a parallelogram, then the parallelogram is a rhombus

Theorem 9-14: If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus

Theorem 9-15: If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle

Section 9-4
Trapezoids and Kites

Theorem 9-16: Case Angles of an Isosceles trapezoid are congruent
Properties of Parallelograms

Theorem 9-1: Opposite sides of a parallelogram are congruent

Theorem 9-2: Opposite angles of a parallelogram are congruent

Angles of a polygon that share a common side are consecutive angles (supplements)

Theorem 9-3: The diagonals of a parallelogram bisect each other (bisects the diagonal, itself, not the angle)

Theorem 9-4: If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal

Section 9-2
proving that quadrilaterals are parallelograms

Theorem 9-5: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram

Theorem 9-6: If one pair of opposite sides of a quarilateral are both congruent and parallel, then the quadrilateral is a parallelogram

Theorem 9-7: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram

Theorem 9-8: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram

Section 9-3
Properties of Special Parallelograms

Theorem 9-9: Each diagonal of a rhombus bisects two <'s of a rhombus

Theorem 9-10: The diagonals of a rhombus are perpendicular

Theorem 9-11: The area of a rhombus is equal to 1/2 the product of the lengths of its diagonals A=1/2 (d1)(d2)

Theorem 9-12: The diagonals of a rectangle are congruent

Theorem 9-13: If one diagonal of a parallelogram bisects 2<'s of a parallelogram, then the parallelogram is a rhombus

Theorem 9-14: If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus

theorem 9-15: If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle

Section 9-4
Trapezoids and Kites

Theorem 9-16: Base angles of an isosceles trapezoid are congruent
Theorem 9-1: Opposite sides of a parallelogram are congruent

Theorem 9-2: Opposite angles of a parallelogram are congruent

Angles of a polygon that share a common side are consecutive angles (supplements)

Theorem 9-3: The diagonals of a parallelogram bisect each other (bisects the diagonal, itself, not the angle)

Theorem 9-4: If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal

Section 9-2
Proving That Quadrilaterals are Parallelograms

Theorem 9-5: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram

Theorem 9-6: If one pair of opposite sides of a quarilateral are both congruent and parallel, then the quadrilateral is a parallelogram

Theorem 9-7: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram

Theorem 9-8: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram

Section 9-3
Properties of Special Parallelograms

Theorem 9-9: Each diagonal of a rhombus bisects two <'s of a rhombus

Theorem 9-10: The diagonals of a rhombus are perpendicular

Theorem 9-11: The area of a rhombus is equal to 1/2 the product of the lengths of its diagonals
A=1/2 (d1)(d2)

Theorem 9-12: The diagonals of a rectangle are congruent

Theorem 9-13: If one diagonal of a parallelogram bisects 2<'s of a parallelogram, then the parallelogram is a rhombus

Theorem 9-14: If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus

Theorem 9-15: If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle

Section 9-4
Trapezoids and Kites

Theorem 9-16: Base angles of an isosceles trapezoid are congruent

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