Proving Quadrilaterals on the Coordinate Plane

What does it mean when two lines are parallel in terms of their slopes?

• They do not intersect

• They have reciprocal slopes

• They have the same slope

• They intersect at a right angle

Which formula is used to find the distance between two points on a coordinate plane?

• Midpoint formula

• Distance formula

• Slope formula

• Perpendicular bisector formula

What is the quickest way to prove a shape is a parallelogram?

• Ensuring all angles are right angles

• Proving that diagonals bisect each other

• Calculating the area

• Checking if all sides are equal

How can you prove that a quadrilateral is a rectangle?

• Ensure that diagonals bisect each other at right angles

• Demonstrate that all angles are 90 degrees

• Show that all sides are of equal length

• Prove that diagonals are congruent and not perpendicular

What must be true for a quadrilateral to be classified as a rhombus?

• Diagonals are congruent

• Diagonals are perpendicular and not congruent

• All sides are parallel

• All angles are equal

In the example provided, what was the first step in proving the shape of the quadrilateral?

• Calculating the area of the shape

• Checking if the sides are parallel

• Graphing the quadrilateral

• Finding the midpoints of the diagonals

What property was used to confirm the shape was a square in the example?

• Both congruent and perpendicular diagonals

• Perpendicular diagonals

• Congruent diagonals

• Equal side lengths

Which method is not suitable for proving a trapezoid?

• Checking for one pair of parallel sides

• Calculating the distances of the legs

• Using the slope formula

• Ensuring all sides are congruent

What additional property distinguishes an isosceles trapezoid from a regular trapezoid?

• All sides are equal

• One pair of parallel sides

• Congruent diagonals

• Congruent non-parallel sides

How do you find the missing vertex point D in a parallelogram using the coordinates of other vertices?

• Using the midpoint formula

• Applying the distance formula

• Calculating changes in x and y values

• Drawing the shape on a graph