Properties and Theorems of Rhombuses

This video tutorial introduces the concept of a rhombus, comparing it to a parallelogram. It covers the properties of rhombus sides, angles, and diagonals, highlighting unique features such as equal sides, opposite equal angles, and diagonals that bisect at 90 degrees. The tutorial also includes practice examples to reinforce understanding of these properties.

What is a key difference between a rhombus and a parallelogram?

• A rhombus has no equal angles.

• A parallelogram has all angles equal.

• A rhombus has no parallel sides.

• All sides of a rhombus are equal.

Which of the following is true about the sides of a rhombus?

• Only two sides are equal.

• All four sides are equal.

• No sides are equal.

• Only opposite sides are equal.

How are the opposite angles in a rhombus related?

• They are always 90 degrees.

• They are supplementary.

• They are equal to each other.

• They are complementary.

What is true about the diagonals of a rhombus?

• They bisect each other at 90 degrees.

• They are equal in length.

• They do not intersect.

• They are parallel.

What special property do the diagonals of a rhombus have?

• They are perpendicular bisectors.

• They are equal in length.

• They do not bisect each other.

• They form acute angles.

In a rhombus, what is true about the corner angles?

• They are not bisected.

• They are bisected by the diagonals.

• They are all 90 degrees.

• They are all equal.

If a rhombus has a side length of 13 and a diagonal of 20, what is the length of half of the diagonal?

• 13

• 20

• 15

• 10

What is the measure of angle x if it is opposite an angle of 40 degrees in a rhombus?

• 110 degrees

• 90 degrees

• 40 degrees

• 70 degrees

In a rhombus, if one diagonal is 20, what is the length of each segment formed by the diagonal?

• 5

• 10

• 15

• 20

What theorem is used to find the length of a side in a right triangle formed by the diagonals of a rhombus?

• Cosine Rule

• Sine Rule

• Triangle Sum Theorem

• Pythagorean Theorem