Understanding Rhombuses in Geometry

This video tutorial by Kirk Weiler covers the properties and characteristics of rhombuses, a type of quadrilateral with four equal sides. The lesson includes proofs that all rhombuses are parallelograms and explores unique properties such as perpendicular diagonals and angle bisectors. The video also provides application problems to reinforce these concepts, concluding with a summary and a preview of the next lesson on squares.

What is a defining characteristic of a rhombus?

• All angles are right angles

• All sides are of equal length

• It has two pairs of parallel sides

• It has one pair of parallel sides

Why can a rhombus be considered a special type of parallelogram?

• Because it has one pair of parallel sides

• Because all its sides are congruent

• Because it has two pairs of parallel sides

• Because it has four right angles

What theorem is used to prove that triangles within a rhombus are congruent?

• Angle-Side-Angle

• Side-Angle-Side

• Side-Side-Side

• Angle-Angle-Side

Which of the following is true about the triangles formed by the diagonals of a rhombus?

• They are all right triangles

• They are all congruent

• They are all scalene

• They are all isosceles

What is a unique property of the diagonals in a rhombus?

• They are congruent

• They are equal in length

• They bisect each other at right angles

• They are parallel

How do the diagonals of a rhombus affect its angles?

• They bisect the angles of the rhombus

• They make opposite angles supplementary

• They make all angles equal

• They make adjacent angles equal

What is the relationship between the diagonals of a rhombus and its angles?

• Diagonals are equal and bisect the angles

• Diagonals are perpendicular and bisect the angles

• Diagonals are congruent and bisect the angles

• Diagonals are parallel and bisect the angles

If a rhombus has diagonals of lengths 10 and 24, what is the length of each side?

• 13

• 15

• 19

• 17

What is the perimeter of a rhombus with diagonals measuring 10 and 24?

• 40

• 72

• 52

• 60

In a rhombus, if one angle is 67 degrees, what is the measure of the adjacent angle?

• 113 degrees

• 67 degrees

• 90 degrees

• 46 degrees