1. 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.
12/28/2018
Section 4.2 Nack

2. 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.
12/28/2018
Section 4.2 Nack

3. 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!
12/28/2018
Section 4.2 Nack