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.
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.
- 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.
- 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.
- 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.
|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|
- Rhombus. All sides are equal and opposite sides are parallel. The diagonals bisect each other at right angles.
- 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.
- 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