This document discusses different ways to prove that a quadrilateral is a parallelogram, including: if both pairs of opposite sides are congruent; if an angle is supplementary to its consecutive angles; if both pairs of opposite angles are congruent; if the diagonals of a quadrilateral bisect each other; or if one pair of opposite sides is both congruent and parallel. It provides examples of each theorem and assigns practice problems for students to complete.

1. Chapter 6
Polygons and
Quadrilaterals
6-3 Proving That a Quadrilateral Is a
Parallelogram

2. Objective
 I can prove that certain quadrilaterals are
parallelograms.

3. Statements Reasons
If both pairs of opposite sides of a quadrilateral are
congruent, then the quadrilateral is a parallelogram.
1
23
4
Q R
T S
;TS QR TQ SR Given:
Prove: Quad. QRST is a 
1. Draw auxiliary line 1. Through any two points
there is exactly one line.
What proof could you come up with to finish this?
QS
Theorem 6-8

4. Theorem 6-9
 If an angle of a quadrilateral is
supplementary to both of its consecutive
angles, then the quadrilateral is a
parallelogram.
A
B C
D
∠𝐴 is supplementary to ∠𝐵
∠𝐴 is supplementary to ∠𝐷

5. O
S T
P
Theorem 6-10
 If both pairs of opposite angles of a
quadrilateral are congruent, then the
quadrilateral is a parallelogram.

6. Theorem 6-11
If the diagonals of a quadrilateral bisect each
other, then the quadrilateral is a
parallelogram.
O
S T
P

7. Theorem 6-12
 If one pair of opposite sides of a quadrilateral
are both congruent and parallel, then the
quadrilateral is a parallelogram.

9. Practice Assignments
 CW: p. 173 1-9, p. 175 19-22
 Have checked by the end of class.
 HW: Worksheet