Proving Properties of Rectangles and Rhombuses in Coordinate Geometry

The video tutorial covers the properties and proofs of rectangles and rhombuses. It begins with an overview of the properties of rectangles and rhombuses, emphasizing their classification as parallelograms. The tutorial then provides a step-by-step guide to proving a quadrilateral is a rectangle by demonstrating it is a parallelogram with one right angle. It also explains how to prove a quadrilateral is a rhombus by showing all sides are congruent using the distance formula or Pythagorean theorem.

What is a unique property of a rectangle that differentiates it from other parallelograms?

• Opposite sides are parallel

• All angles are right angles

• Diagonals bisect each other

• All sides are congruent

Which formula is used to calculate the slope of a line segment?

• y1 - y2 over x1 - x2

• x1 - x2 over y1 - y2

• y2 - y1 over x2 - x1

• x2 - x1 over y2 - y1

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

• Two pairs of opposite sides are parallel

• All angles are right angles

• Diagonals are equal

• All sides are congruent

How do you prove that sides are parallel using slopes?

• Show that the slopes are zero

• Show that the slopes are negative reciprocals

• Show that the slopes are equal

• Show that the slopes are undefined

What is the slope of a line segment if it rises 2 units and runs 4 units?

• 1/2

• 2

• 1/4

• 4

Why is it sufficient to prove only one right angle to confirm a rectangle?

• Because consecutive angles are supplementary

• Because opposite angles in a parallelogram are congruent

• Because all sides are congruent

• Because diagonals bisect each other

What is the first step in proving a quadrilateral is a rhombus?

• Show opposite sides are parallel

• Show diagonals bisect each other

• Show all sides are congruent

• Show all angles are right angles

Which method is preferred by the instructor to prove the sides of a rhombus are congruent?

• Using the midpoint formula

• Using the slope formula

• Using the distance formula

• Using the area formula

What is the length of side AB if it forms a 3-4-5 right triangle?

• 6

• 4

• 3

• 5

What is the final conclusion if all four sides of a quadrilateral are congruent?

• It is a parallelogram

• It is a square

• It is a rectangle

• It is a rhombus