Proving Properties of Quadrilaterals with Analytic Geometry

The lesson demonstrates how to verify properties of quadrilaterals by plotting points and calculating midpoints. It shows how to prove a quadrilateral is a parallelogram using the slope formula and explores identifying a kite by comparing side lengths. The lesson concludes with proving the perpendicularity of diagonals in a kite.

What is the midpoint formula used to find the coordinates of a point?

• (x1 + x2) / 2, (y1 + y2) / 2

• (x1 + x2, y1 + y2)

• (x1 * x2) / 2, (y1 * y2) / 2

• (x1 - x2) / 2, (y1 - y2) / 2

Which coordinates correctly represent the midpoint of side AB?

• (0, 4.5)

• (0, 9.5)

• (1, 4.5)

• (1, 9.5)

How do you prove that a quadrilateral is a parallelogram using the slope formula?

• Show that no sides have equal slopes.

• Show that all sides have equal slopes.

• Show that adjacent sides have equal slopes.

• Show that opposite sides have equal slopes.

What is the slope of side FG in the parallelogram?

• 0

• 1/12

• -4/3

• 3/4

What defines a kite in geometry?

• A quadrilateral with two pairs of adjacent sides of equal length.

• A quadrilateral with opposite sides of equal length.

• A quadrilateral with all sides of equal length.

• A quadrilateral with no equal sides.

What is the result of the distance formula calculation for side PQ?

• Root of 89

• Root of 17

• Root of 25

• Root of 64

What is the length of side QR in the kite?

• Root of 17

• Root of 25

• Root of 64

• Root of 89

How can you verify that two line segments are perpendicular?

• Their slopes are unrelated.

• Their slopes are equal.

• Their slopes are negative reciprocals.

• Their slopes are positive reciprocals.

What is the slope of diagonal PR in the kite?

• Undefined

• -1

• 1

• 0

What is the slope of diagonal QS in the kite?

• -1

• 1

• 0

• Undefined