4.2: The Parallelogram and the Kite Theorems on Parallelograms Theorem 4.2.1: If two sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram. Proof p. 187 Theorem 4.2.2: If both pairs of opposite sides of a quadrilateral are congruent, then it is a parallelogram. Theorem 4.2.3: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Summary: We know a quadrilateral is a parallelogram if: Two sides are congruent AND parallel Both pairs of opposite sides are congruent Diagonals bisect each other. 11/9/2018 Section 4.2 Nack

The Kite A Kite is a quadrilateral with two distinct pairs of congruent adjacent sides. (Distinct = does not have 4 congruent sides!) Theorem 4.2.4: In a kite, one pair of opposite angles are congruent. B  D p. 189 Additional Theorems: One diagonal is the perpendicular bisector of the other diagonal. One diagonal of a kite bisects two of the angles of the kite. 11/9/2018 Section 4.2 Nack

Additional Triangle Theorem Theorem 4.2.5: The segment that joins the midpoints of two sides of a triangle is parallel to the third side and has a length equal to one-half the length of the third side. Proof p. 190 of the parallel section of the proof. Note: This proof requires a construction! 11/9/2018 Section 4.2 Nack