Section 4.6 – Conditions for Special Quadrilateral

Theorem] If 2 pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram

Theorem] If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram

Theorem] If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram

Theorem] If one angle of a parallelogram is a right angle, then the parallelogram is a rectangle

Theorem] If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle (Housebuilder Theorem)

Theorem] If one pair of adjacent sides of a parallelogram are congruent, then the parallelogram is a rhombus

Theorem] If the diagonals of a parallelogram bisect the angles of the parallelogram, then the parallelogram is a rhombus

Theorem] If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus

Other Theorems

Theorem] A midsegment of a triangle is parallel to a side of the triangle and has a measure equal to half of the measure of that side