Proving Parallelograms with Coordinate Geometry

The video tutorial discusses coordinate proofs to demonstrate that quadrilaterals are parallelograms. It covers key concepts like slope, midpoint, and distance formulas, and explains three methods to prove a quadrilateral is a parallelogram: using the definition, congruent sides, and bisecting diagonals. The tutorial includes detailed examples for each method, showing how to apply these concepts to solve problems.

What are the three key calculations used in coordinate proofs?

• Slope, midpoint, and distance formulas

• Integration, differentiation, and limits

• Area, perimeter, and volume formulas

• Addition, subtraction, and multiplication

Which formula is used to prove that two lines are congruent?

• Area formula

• Distance formula

• Midpoint formula

• Slope formula

What does the midpoint formula help to determine?

• The midpoint of a line segment

• The slope of a line

• The length of a line segment

• The area of a triangle

How can you prove that two lines are parallel using the slope formula?

• By showing they have the same slope

• By showing they have the same length

• By showing they intersect at a right angle

• By showing they have the same midpoint

What is the first method to prove a quadrilateral is a parallelogram?

• Using the definition of parallelogram

• Using the area formula

• Using the volume formula

• Using the perimeter formula

How can you prove that opposite sides of a quadrilateral are congruent?

• By using the slope formula

• By using the area formula

• By using the distance formula

• By using the midpoint formula

What is the third method to prove a quadrilateral is a parallelogram?

• Showing that all sides are equal

• Showing that diagonals bisect each other

• Showing that the area is the same

• Showing that all angles are right angles

What is the slope of a line segment if the coordinates are (1, 3) and (3, 5)?

• 2

• 1

• 3

• 4

What is the length of a line segment if the coordinates are (1, 3) and (3, 5)?

• Square root of 8

• Square root of 10

• Square root of 12

• Square root of 14

What is the midpoint of a line segment if the coordinates are (1, 3) and (9, 1)?

• (4, 3)

• (5, 3)

• (4, 2)

• (5, 2)