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

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Presentation transcript:

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

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

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

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

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

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

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

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

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

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

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

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

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

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