# Are consecutive angles of a parallelogram supplementary?

DEFINITION: A

**parallelogram**is a quadrilateral with both pairs of**opposite**sides parallel. THEOREM: If a quadrilateral has 2 sets of**opposite angles**congruent, then it is a**parallelogram**. * THEOREM: If a quadrilateral has**consecutive angles**which are**supplementary**, then it is a**parallelogram**.A.

### Do consecutive interior angles equal 180?

The

**consecutive interior angles**theorem states that when the two lines are parallel, then the**consecutive interior angles**are supplementary to each other. Supplementary means that the two**angles add up to 180**degrees.#### What is another name for consecutive interior angles?

When two lines are crossed by another line (which is called the Transversal), the pairs of**angles**: • on one side of the transversal. • but inside the two lines. are called**Consecutive Interior Angles**. When the two lines are parallel the**Consecutive Interior Angles**add to 180 degrees.#### Are consecutive exterior angles supplementary?

Two**angles**that are**exterior**to the parallel lines and on the same side of the transversal line are called same-side**exterior angles**. The theorem states that same-side**exterior angles**are**supplementary**, meaning that they have a sum of 180 degrees.#### What are consecutive angles of a parallelogram?

Opposite angels are congruent (D = B). Consecutive angles are supplementary (A + D =**180°**). If one angle is right, then all angles are right. The diagonals of a parallelogram bisect each other.

B.

### Which quadrilateral always have consecutive angles that are supplementary?

Quadrilaterals

A | B |
---|---|

in these quadrilaterals, the diagonals are congruent | rectangle, square, isosceles trapezoid |

in these quadrilaterals, each of the diagonals bisects a pair of opposite angles | rhombus, square |

in these quadrilaterals, the diagonals are perpendicular | rhombus, square |

a rhombus is always a | parallelogram |

#### Which quadrilaterals have diagonals that bisect each other at right angles?

**Rhombus**. All sides are equal and opposite sides are parallel. The diagonals bisect each other at right angles.#### What properties do rhombuses and parallelograms share?

The**rectangle**has the following properties: All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite sides are congruent, and diagonals bisect each other). All**angles**are right**angles**by**definition**. The diagonals are congruent.#### Which quadrilaterals have two pairs of parallel sides?

It is also a**parallelogram**, since it has two pairs of parallel sides. A**square**has two pairs of parallel sides, four right angles, and all four sides are equal. It is also a**rectangle**and a**parallelogram**. A**rhombus**is defined as a**parallelogram**with four equal sides.

Updated: 2nd October 2019