4 2 The Parallelogram and the Kite Theorems

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 Read Strategy 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. 12/7/2020 Section 4. 2 Nack 1

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. 188 Ex. 2 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. 12/7/2020 Section 4. 2 Nack 2

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. Ex 4 p. 191 • Note: This proof requires a construction! 12/7/2020 Section 4. 2 Nack 3