Properties and Proofs of Parallelograms

Drew Moyer explains how to organize coordinate proofs in geometry by proving a quadrilateral is a parallelogram. The video demonstrates calculating slopes to show that opposite sides are parallel, thus confirming the shape's properties.

What is the main goal of a coordinate proof in geometry?

• To calculate the perimeter of a shape

• To draw a shape accurately

• To prove properties using variables for coordinates

• To find the area of a shape

What must be shown to prove a quadrilateral is a parallelogram?

• All angles are right angles

• All sides are equal

• Diagonals are equal

• Both pairs of opposite sides are parallel

How is the slope of a line segment calculated?

• By dividing the difference in x-coordinates by the difference in y-coordinates

• By adding the x-coordinates and y-coordinates

• By dividing the difference in y-coordinates by the difference in x-coordinates

• By multiplying the x-coordinates and y-coordinates

What is the slope of line segment LM?

• Z

• Undefined

• 1

• 0

What does a slope of 0 indicate about a line?

• It is vertical

• It is horizontal

• It is diagonal

• It is undefined

What is the slope of line segment ON?

• Z

• 0

• 1

• Undefined

What is the slope of line segment OL?

• 0

• L/M

• M/L

• Undefined

What is the slope of line segment NM?

• M/L

• L/M

• 0

• Undefined

If two lines have the same slope, what can be concluded?

• They are perpendicular

• They are skew

• They are parallel

• They intersect

What is the final conclusion about quadrilateral LMNO?

• It is a rectangle

• It is a square

• It is a parallelogram

• It is a trapezoid