Understanding Rhombuses

The video tutorial focuses on the properties of a rhombus, a special type of quadrilateral. It explains that a rhombus is a parallelogram with all sides congruent and opposite angles equal. The video covers how diagonals bisect each other at right angles and how to calculate the area and perimeter of a rhombus using its diagonals. Several example problems are solved to illustrate these concepts, including determining missing angles and side lengths using the Pythagorean theorem.

Which of the following is a property of a rhombus?

• Diagonals are equal in length.

• Opposite sides are parallel.

• All angles are right angles.

• It has five sides.

What is true about the diagonals of a rhombus?

• They bisect each other at right angles.

• They are parallel to each other.

• They are equal in length.

• They do not intersect.

How do you calculate the area of a rhombus?

• Base times height

• Side squared

• One half the product of the diagonals

• Sum of all sides

If the diagonals of a rhombus are 8 and 6, what is the area?

• 30 square units

• 24 square units

• 48 square units

• 14 square units

In a rhombus, if one angle is 30 degrees, what is the measure of the angle adjacent to it?

• 120 degrees

• 90 degrees

• 150 degrees

• 60 degrees

What is the relationship between the diagonals and the angles they bisect in a rhombus?

• Diagonals make angles supplementary.

• Diagonals make angles complementary.

• Diagonals do not affect angles.

• Diagonals bisect angles into equal parts.

If AE = 3x + 1 and EC = 5x - 9 in a rhombus, what is the value of x?

• x = 7

• x = 9

• x = 3

• x = 5

In a rhombus, if AB = y^2 + 1 and BC = 3y + 5, what is a possible value of y?

• y = 8

• y = 2

• y = 4

• y = 6

What is the formula for the perimeter of a rhombus?

• Side length squared

• Sum of the diagonals

• 4 times the side length

• Twice the sum of the diagonals

If the diagonals of a rhombus are 16 and 30, what is the area?

• 60 square units

• 480 square units

• 240 square units

• 120 square units