Understanding Rhombus Properties and Proofs

The video tutorial explains how to prove a quadrilateral is a rhombus. It begins by discussing the properties of a rhombus, such as diagonals bisecting at right angles. The tutorial then demonstrates how to prove a shape is a parallelogram by finding the midpoints of diagonals. Next, it shows how to prove the diagonals intersect at 90 degrees using gradient calculations. Finally, alternative methods for proving a rhombus, such as using the distance formula to show equal adjacent sides, are discussed.

What is one key property of a rhombus that is essential for proving it?

• All angles are equal

• Diagonals bisect at right angles

• All sides are different

• It has one pair of parallel sides

Which formula is used to find the midpoint of a diagonal?

• Distance formula

• Slope formula

• Midpoint formula

• Area formula

What conclusion can be drawn if the midpoints of the diagonals are the same?

• The shape is a trapezoid

• The shape is a square

• The shape is a parallelogram

• The shape is a rectangle

What condition must be met for diagonals to bisect at right angles?

• The gradients are equal

• The product of the gradients is -1

• The sum of the gradients is zero

• The gradients are both positive

What is the gradient of diagonal AC if y2 - y1 = 8 and x2 - x1 = -8?

• 0

• 8

• -1

• 1

What is the final conclusion about the quadrilateral ABCD?

• It is a trapezoid

• It is a rectangle

• It is a square

• It is a rhombus

Which method can be used to prove a quadrilateral is a rhombus by checking side lengths?

• Area formula

• Slope formula

• Distance formula

• Midpoint formula

What is another way to prove a quadrilateral is a rhombus besides using diagonals?

• Proving all sides are equal

• Proving all angles are 90 degrees

• Proving it is a rectangle

• Proving it has one pair of parallel sides

What is the significance of finding equal adjacent sides in a quadrilateral?

• It proves the shape is a rectangle

• It proves the shape is a square

• It proves the shape is a trapezoid

• It provides evidence the shape is a rhombus

What is the result if the product of the gradients of the diagonals is -1?

• The diagonals are parallel

• The diagonals are perpendicular

• The diagonals are equal

• The diagonals are not related