Proving Quadrilaterals Using Distance and Slope Formula

Which formula is used to show that lengths are parallel or perpendicular?

• Slope

• Midpoint

• Distance

Which formula is used to show that lengths are equal?

• Slope

• Midpoint

• Distance

Tags

CCSS.HSG.GPE.B.7

To prove that Quadrilateral JKLM is a parallelogram, given the coordinates of its vertices, Josue decided to show that opposite sides are congruent. To do so, which calculation must Sue perform?

• Find the lengths of the sides using the distance formula.

• Find the slope of each side using the distance formula.

• Find the midpoint of each diagonal.

• Find the length of each side using the slope formula.

Tags

CCSS.HSG.CO.B.7

To prove Quadrilateral JKLM is a parallelogram, given the coordinates of its vertices. Selvin decided to show that both pairs of opposite sides are parallel. To do so, which calculation must Juan perform?

• Find the slope of 2 sides.

• Find the slope of all 4 sides.

• Find the slope of the diagonals.

• Find the length of all 4 sides.

Tags

CCSS.6.G.A.3

To prove that the parallelogram JKLM is a rectangle, given its coordinates of its vertices. Yasmin decided to show that both pairs of sides are congruent and the diagonals are congruent. To do so, which calculation must Yasmin perform?

• Find the slope of all 4 sides and the diagonals using the distance formula.

• Find the midpoint of all 4 sides and the diagonals.

• Find the length of all 4 sides and the 2 diagonals using the distance formula.

• Find the length of 2 sides and the diagonals using the slope formula.

Tags

CCSS.HSG.CO.C.11

To prove that the parallelogram JKLM is a rectangle, given the coordinates of its vertices. Luis decided to show that two adjacent sides form perpendicular lines. To do so, which calculations must Luis perform?

• Find the slope of two adjacent sides.

• Find the slope of all 4 sides.

• Find the slope of the diagonals.

• Find the length of two consecutive sides using the distance formula.

Tags

CCSS.HSG.CO.C.11

To prove that a parallelogram QRST is a square, given the coordinates of its vertices, Aylin decided to show that the sides form perpendicular lines and all sides are congruent. To do so, which calculation must Aylin perform?

• Find the length of all 4 sides using the distance formula.

• Find the length of all 4 sides using the distance formula and use the slope formula for 2 adjacent sides.

• Find the slope of 2 sides.

• Find the slope of all 4 sides and the length of 2 sides.

Tags

CCSS.HSG.GPE.B.7

To prove that the quadrilateral RHOM is a rhombus, given the coordinates of its vertices, Lesley and Angelis decided to show that all sides are congruent. To do so, which calculation must Lesley and Angelis perform?

• Find the slope of any 2 consecutive sides using the slope formula.

• Find the length of all 4 sides using the distance formula.

• Find the slope of all 4 sides using the slope formula.

• Find the midpoint of all 4 sides using the distance formula.

Tags

CCSS.HSG.CO.B.7

To prove that Quadrilateral JKLM is a trapezoid, given the coordinates of the vertices, Nayeli decided to show that there is only one pair of parallel sides and the non-parallel sides are congruent. To do so, which calculation must Nayeli make?

• Find the length of all the sides.

• Find the length of the 4 sides and slope of 2 sides.

• Find the slope of 4 sides and the length of 2 sides.

• Find the slope of all the sides.

Tags

CCSS.6.G.A.3

To prove that Triangle ABC is a right triangle, given the coordinates of the vertices, Angie decided to show that there is two sides that are perpendicular. To do so, which calculation must Angie make?

• Find the length of all the sides.

• Find the slope of all the sides.

• Find the length of two sides.

• Find the midpoint.