Prove Diagonals of a Quadrilateral Bisect Each Other

Which theorem can be used to prove the quadrilateral is a parallelogram?

• Parallelogram Opposite Sides Converse Theorem

• Parallelogram Opposite Angles Converse Theorem

• Opposite Sides Parallel and Congruent Theorem

• Parallelogram Diagonals Converse Theorem

State which method we can use to show that the quadrilateral is a parallelogram. 

• Both pairs of opposite angles are congruent.

• Both pairs of opposite sides are congruent.

• Both pairs of diagonals bisect each other.

• Both pairs of opposite sides are parallel. 

Which statement about parallelograms is always true?

• The diagonals are congruent.

• The diagonals bisect each other.

• The diagonals are perpendicular.

• The diagonals bisect their respective angles.

Is this quadrilateral a parallelogram?

• Yes. Diagonals bisect each other

• no

• Yes. Opposite angles are congruent

• Yes. Opposite sides are congruent

Determine the property being used to solve the problem.

• Opposite SIDES are congruent

• Opposite ANGLES are congruent

• Consecutive angles are supplementary

• Diagonals bisect each other

Determine the property being used to solve the problem.

• Opposite SIDES are congruent

• Opposite ANGLES are congruent

• Consecutive angles are supplementary

• Diagonals bisect each other

Quadrilateral ABCD has diagonals AC and BD. Which information is NOT sufficient to prove ABCD is a parallelogram?  SKETCH AND MARK-UP A DIAGRAM FOR EACH OF THE ANSWER CHOICES.

• AC and BD bisect each other.

State which method we can use to show that the quadrilateral is a parallelogram.

• Both pairs of opposite angles are congruent.

• Both pairs of opposite sides are congruent.

• The diagonals bisect each other.

• Both pairs of opposite sides are parallel.

Which theorem shows that the quadrilateral is a parallelogram?

• Diagonals bisect eachother

• Opposite Sides Congruent

• Opposite Angles Congruent

• 1 set of Opposite Sides is Parallel and Congruent

ABCD is a parallelogram, so the diagonals bisect each other. What is the midpoint of the diagonals?

• (a+c,b)

• (c/2,b/2)

• ((a+c)/2,b/2)

• (a/2,b/2)