Properties of a Parallelogram - Warm Up/Cool Down

Opposite sides of a parallelogram are __________________.

• congruent

• parallel

• perpendicular

• consecutive

Answer explanation

In a parallelogram, opposite sides are both congruent and parallel. Congruent means they have the same length, and parallel means they run in the same direction without intersecting. So, the correct answer is that opposite sides of a parallelogram are congruent and parallel. However, among the given options, only 'congruent' and 'parallel' are correct.

The diagonals of a parallelogram always ... 

• are congruent

• are perpendicular

• bisect each other

• are parallel

Answer explanation

The correct answer is 'bisect each other'. In a parallelogram, the diagonals intersect each other at their midpoints, effectively bisecting each other. This means each diagonal is divided into two equal parts by the other diagonal. The other options are not always true for a parallelogram.

In a parallelogram, opposite angles are ________.

• congruent

• supplementary

• consecutive

• parallel

Answer explanation

In a parallelogram, opposite angles are congruent. This means that they have the same measure. This property is a result of the parallel sides of the parallelogram, which create equal angle measures when they intersect with the other pair of parallel sides.

Consecutive angles of parallelograms are ______.

• bisected

• congruent

• supplementary

• complementary

Answer explanation

In a parallelogram, consecutive angles are always supplementary. Supplementary angles are two angles that add up to 180 degrees. Therefore, the correct answer to the question is 'supplementary'.

Tags

CCSS.HSG.CO.C.11

Name the angle relationship and state whether they are congruent or supplementary.

• Alternate Interior angles are Congruent

• Alternate Exterior angles are Congruent

• Alternate Interior angles are supplementary

• Alternate Exterior Angles are supplementary

Answer explanation

The angle relationship in the question is 'Alternate Interior angles are congruent'. Alternate interior angles are formed when a transversal intersects two parallel lines. These angles are located on opposite sides of the transversal and are inside the parallel lines. They are congruent, meaning they have the same measure.

Tags

CCSS.8.G.A.5