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.