6.2 Properties of Parallelograms

Front

What is a parallelogram?

Back

A parallelogram is a four-sided figure (quadrilateral) with opposite sides that are parallel and equal in length.

Front

What are the properties of the opposite angles in a parallelogram?

Back

The opposite angles in a parallelogram are equal.

Front

What is the sum of the interior angles of a parallelogram?

Back

The sum of the interior angles of a parallelogram is 360 degrees.

Front

In a parallelogram, what can be said about the diagonals?

Back

The diagonals of a parallelogram bisect each other.

Front

What is the relationship between adjacent angles in a parallelogram?

Back

Adjacent angles in a parallelogram are supplementary, meaning they add up to 180 degrees.

Front

If one angle of a parallelogram is 70 degrees, what are the measures of the other angles?

Back

The opposite angle is also 70 degrees, and the adjacent angles are 110 degrees each.

Front

What is the formula for the area of a parallelogram?

Back

The area of a parallelogram is given by the formula: Area = base × height.

Front

How do you find the length of the diagonals in a parallelogram?

Back

The lengths of the diagonals can be found using the formula: d = √(a² + b² - 2ab cos(θ)), where a and b are the lengths of the sides and θ is the angle between them.

Front

What is the significance of the diagonals being bisected in a parallelogram?

Back

The bisection of diagonals indicates that the two triangles formed by the diagonals are congruent.

Front

If the sides of a parallelogram are 5 cm and 12 cm, what is the maximum length of the diagonal?

Back

The maximum length of the diagonal can be found using the triangle inequality, which states it cannot exceed the sum of the lengths of the two sides, so it is less than 17 cm.