Table of Contents
How do you know if a quadrilateral is a parallelogram?
If both pairs of opposite sides of a quadrilateral are parallel, then it’s a parallelogram (reverse of the definition). If both pairs of opposite sides of a quadrilateral are congruent, then it’s a parallelogram (converse of a property).
Why is the quadrilateral a parallelogram?
DEFINITION: A parallelogram is a quadrilateral with both pairs of opposite sides parallel. THEOREM: If a quadrilateral has diagonals which bisect each other, then it is a parallelogram. * THEOREM: If a quadrilateral has one set of opposite sides which are both congruent and parallel, then it is a parallelogram.
What does a quadrilateral parallelogram look like?
Parallelogram: A quadrilateral that has two pairs of parallel sides. Rhombus: A quadrilateral with four congruent sides; a rhombus is both a kite and a parallelogram. Rectangle: A quadrilateral with four right angles; a rectangle is a type of parallelogram.
How do you make a quadrilateral a parallelogram?
How To Prove a Parallelogram? 17 Step-by-Step Examples For Mastery!
- Both pairs of opposite sides are parallel.
- Both pairs of opposite sides are congruent.
- Both pairs of opposite angles are congruent.
- Diagonals bisect each other.
- One angle is supplementary to both consecutive angles (same-side interior)
How do you know if a shape is a quadrilateral?
Quadrilaterals: Classification
- A quadrilateral is a polygon with four sides.
- A rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals.
- A rhombus is a parallelogram with four congruent sides.
- A trapezoid is a quadrilateral with exactly one pair of parallel sides.
How many quadrilaterals are parallelograms?
| Name of Quadrilateral | Description |
|---|---|
| Parallelogram | 2 pairs of parallel sides. Opposite sides and opposite angles are congruent. |
| Rectangle | 2 pairs of parallel sides. 4 right angles (90°). Opposite sides are parallel and congruent. All angles are congruent. |
How do you prove something is a quadrilateral?
Here are the six ways to prove a quadrilateral is a parallelogram:
- Prove that opposite sides are congruent.
- Prove that opposite angles are congruent.
- Prove that opposite sides are parallel.
- Prove that consecutive angles are supplementary (adding to 180°)
- Prove that an angle is supplementary to both its consecutive angles.
Is a parallelogram always a quadrilateral?
Explanation: A Quadrilateral is only a 4 sided figure & has no specific features, whereas a Parallelogram is a 4 sided figure with opposite sides parallel and equal, opposite angles equal and adjacent angles in a linear pair. A Quadrilateral is not a Parallelogram. A Parallelogram is a Quadrilateral.