1. Proving a quadrilateral is a Parallelogram

2. How do we know if a Quadrilateral is a Parallelogram?

3. How do we know if a Quadrilateral is a Parallelogram?
If it has two sets of parallel sides, then it is a parallelogram. (Definition)
There are 4 other sets of conditions that show a quadrilateral is a parallelogram by logical conclusion.
The diagonals bisect each.
The opposite sides are congruent
The opposite angles are congruent
One pair of sides is both congruent and parallel.

4. Prove that if a quadrilateral’s opposite sides are congruent,then it is a parallelogram.
A D STATEMENTS REASONS C
Given: AB = CD
BC = DA
Prove: ABCD is a
parallelogram B

5. Prove that if a quadrilateral’s diagonals bisect each other,then it is a parallelogram.
A D STATEMENTS REASONS C
Given: AE = CE
BE = DE
Prove: ABCD is a
parallelogram E B

6. Is there enough information to determine if the quadrilateral is a parallelogram?
A D 1. AB = DC, AB ll DC
Yes.
C 2. BE = ED, AB = CD
No.
3.<DAC=<BCA,<BAC=DCA E B

7. Homework
P 307 (7-15,20-29,32-34)