Proving Quadrilaterals Coordinate

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.

If you want to prove that Quadrilateral ABCD is a square, SELECT ALL the pieces of evidence you would need to use.

• The length of each side is √(68), therefore all sides are congruent

• The slope of AC and BD are both 1/4, therefore AC is parallel to BD

• The slopes of AC and CD are opposite reciprocals, therefore AC is perpendicular to CD

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

• Find the length of all 4 sides.

• Find the length of both diagonals.

• Find the slope of both diagonals

• Find the slope of all 4 sides.

• Find the length of 2 consecutive sides

• Find the slope of two consecutive sides

• Find the length of all 4 sides

• Find the length of two opposite sides

• mAB ∙ mBC = -1

• AB = CD

• AB = BC

• mAB = mBC

How would you prove a quadrilateral is a rhombus using distance formula?

• Prove diagonals are perpendicular

• Prove there are 4 congruent sides

• Prove opposite sides are parallel

• Prove there are 4 right angles

Brad proved that ABCD is a parallelogram and that all sides had the same distance What should he do next if he wants to prove it is a square?

• He doesn't need to do anything else, it looks like a square so he is all set. 

• Compare the slopes of adjacent sides to see if they are perpendicular. 

How would you prove a quadrilateral is a rectangle using distance formula?

• Prove diagonals are congruent

• Prove there are 4 right angles

• Prove opposite angles are congruent

• Prove opposite sides are parallel