Proving Quadrilaterals Algebraically

If you wanted to prove that Quadrilateral ABCD is a Parallelogram, what would be the best piece of evidence to use?

• Length of AC = Length of BD, therefore Side AC is congruent to Side BD

• Length of AC = Length of BD, therefore Side AC is parallel to Side BD

• Slope of AC = Slope of BD, therefore Side AC is parallel to Side BD

• The Slopes of AC and BD are opposite reciprocals, therefore Side AC is parallel to Side BD

If you wanted to prove that Quadrilateral ABCD is a rhombus, what would be the best piece of evidence to use?

• The length of each side is √(34), therefore all sides are congruent.

• The length of each side 8, therefore all sides are congruent.

• The slope of AC and BD is 5/3, therefore AC and BD are parallel.

• The slopes of the sides are opposite reciprocals, therefore opposite sides are parallel.

If you want to prove that Quadrilateral ABCD is a rectangle, what is the best piece of evidence to use?

• The lengths of AC and BD are the same, therefore AC and BD are congruent

• The slopes of AC and BD are the same, therefore AC and BD are congruent

• The slopes of AB and BD are the same, therefore AC is perpendicular to BD

• The slopes of AB and BD are opposite reciprocals, therefore AC is perpendicular to BD.

What is the slope of Side AC?

• 2/5

• 5/2

• 5

• √(29)

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

Fill in the missing reason for the proof.

• If alternate interior angles are congruent, then the lines are parallel.

• Definition of parallelogram

• Definition of parallel lines

• Opposite sides of a parallelogram are congruent.

Choose the correct missing reasons for the proof.

• 4) CPCTC; 6)All quads are parallelograms

• 4) Alternate Interior Angles are congruent; 6) Definition of paralelogram

• 4)CPCTC; 6)Definition of parallelogram

• 4) Alternate Interior Angles are congruent; 6) All quads are parallelograms

The missing reason is the same for steps 2 and 4. What is the missing reason?

• If alternate interior angles are congruent, then the lines are parallel.

• If vertical angles are congruent, then the lines are parallel.

• Definition of parallelogram

• Alternate interior angles formed by parallel lines are congruent.

Which method will NOT prove the quadrilateral is a parallelogram.

• Show that a pair of sides are congruent and parallel.

• Show that both pairs of opposite sides are congruent

• Show that both pairs of opposite sides are parallel

• Show that a pair of sides are parallel

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