1. Proving that a quadrilateral is a Parallelogram Geometry Regular Program SY 2014-2015 Source: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson

2. Proving Parallelograms When is a quadrilateral a parallelogram? 1.If both pairs of opposite sides are parallel 2.If both pairs of opposite sides are congruent 3.If both pairs of opposite angles are congruent 4.If the diagonals bisect each other 5.If a pair of opposite sides are both congruent and parallel

3. Exercises Is the quadrilateral a parallelogram or not ? Why? YES!

4. Exercises Is the quadrilateral a parallelogram or not ? Why? YES!

5. Exercises Is the quadrilateral a parallelogram or not ? Why? YES!

6. Exercises Is the quadrilateral a parallelogram or not ? Why? No 

7. Exercises Is the quadrilateral a parallelogram or not ? Why? No 

8. Exercises Is the quadrilateral a parallelogram or not ? Why? No 

9. Exercises Is the quadrilateral a parallelogram or not ? Why? No 

10. Exercises Is the quadrilateral a parallelogram or not ? Why? YES!

11. Exercises Is the quadrilateral a parallelogram or not ? Why? YES!

12. Exercises What must be the values of x and y to make ABCD a parallelogram?

13. Exercises What must be the values of x and y to make ABCD a parallelogram?

14. Exercises What must be the values of x to make ABCD a parallelogram?