Coordinate Geometry Proofs for Parallelograms

The video tutorial introduces coordinate proofs, focusing on proving quadrilaterals as parallelograms using the coordinate plane. It reviews key formulas such as slope, distance, and midpoint, and explains how to determine if slopes are parallel or perpendicular. The tutorial outlines methods for proving parallelograms, emphasizing the use of segments rather than angles. An example is provided to demonstrate the process of proving a quadrilateral is a parallelogram by showing both pairs of opposite sides are parallel.

What type of proof will be introduced in this lesson?

• Paragraph proof

• Indirect proof

• Coordinate proof

• Two-column proof

Which formula is used to determine if two lines are parallel?

• Midpoint formula

• Area formula

• Slope formula

• Distance formula

What is the product of the slopes of two perpendicular lines?

• 1

• Negative one

• Infinity

• 0

If a line has a slope of 1/4, what is the slope of a line perpendicular to it?

• -4

• 1/4

• -1/4

• 4

Which method is NOT used to prove a quadrilateral is a parallelogram on the coordinate plane?

• Diagonals bisect each other

• Opposite angles are congruent

• Opposite sides are parallel

• Opposite sides are congruent

What formula is used to show that diagonals bisect each other?

• Area formula

• Midpoint formula

• Distance formula

• Slope formula

In the example, which pairs of sides are compared to prove they are parallel?

• JK and LM, JM and KL

• JK and JM, KL and LM

• JK and KL, LM and JM

• JK and LM, KL and JM

What is the slope of the line segment JK if J(-1, -4) and K(6, 1)?

• -5/3

• 5/3

• -3/5

• 3/5

What conclusion is drawn if both pairs of opposite sides of a quadrilateral are parallel?

• The quadrilateral is a rhombus

• The quadrilateral is a trapezoid

• The quadrilateral is a parallelogram

• The quadrilateral is a rectangle

What should students do in the second and third examples?

• Prove the quadrilaterals are rhombuses

• Prove the quadrilaterals are parallelograms

• Prove the quadrilaterals are rectangles

• Prove the quadrilaterals are trapezoids