There are 5 ways to prove that a quadrilateral is a parallelogram: If

There are 5 ways to prove that a quadrilateral is a parallelogram: If

5.6-Proving that a Quadrilateral is a
Parallelogram
There are 5 ways to prove that a quadrilateral is a parallelogram:
1. If both pairs of opposite sides of a quadrilateral are parallel, then the
quadrilateral is a parallelogram.
2. If both pairs of opposite sides of a quadrilateral are congruent, then the
quadrilateral is a parallelogram.
3. If one pair of opposite sides of a quadrilateral are both parallel and
congruent, then the quadrilateral is a parallelogram.
4. If the diagonals of a quadrilateral bisect each other, then the
quadrilateral is a parallelogram.
5. If both pairs of opposite angles of a quadrilateral are congruent, then the
quadrilateral is a parallelogram.
Ex 1
Given: ACDF is a parallelogram
AFB  ECD
Prove: FBCE is a parallelogram
Statements
____
|
Reasons
Chapter 5 Page 1
____
.
Ex 2
Given: CAR is isosceles with base CR
AC  BK
C  K
Prove: BARK is a parallelogram
Statements
____
|
Reasons
Chapter 5 Page 2
____
.