Quadrilaterals Theorems

Theorems

• Opposite sides of a parallelogram are congruent.
• Opposite angles of a parallelogram are congruent.
• Diagonals of a parallelogram bisect each other.
• If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
• If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram.
• If both pairs of opposite angles of quadrilateral are congruent, the the quadrilateral is a parallelogram.
• If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
• If two lines are parallel, then all points on one line are equidistant from the other line.
• If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
• A line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side.
• The segment that joins the midpoints of two sides of a triangle (1) is parallel to the third side and (2) is half as long as the third side.
• The diagonals of a rectangle are congruent.
• The diagonals of a rhombus are perpendicular.
• Each diagonal of a rhombus bisects two angles of the rhombus.
• The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.
• If an angle of a parallelogram is a right angle, then the parallelogram is a rectangle.
• If two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus.
• Base angles of an isosceles trapezoid are congruent.
• The median of a trapezoid (1) is parallel to the bases and (2) has a length equal to the average of the base lengths.