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What are the 5 ways to prove that a quadrilateral is a parallelogram?

What are the 5 ways to prove that a quadrilateral is a parallelogram?

There are five ways to prove that a quadrilateral is a parallelogram:

  • Prove that both pairs of opposite sides are congruent.
  • Prove that both pairs of opposite sides are parallel.
  • Prove that one pair of opposite sides is both congruent and parallel.
  • Prove that the diagonals of the quadrilateral bisect each other.

How do you prove that a quadrilateral is a parallelogram?

If both pairs of opposite angles of a quadrilateral are congruent, then it’s a parallelogram (converse of a property). If the diagonals of a quadrilateral bisect each other, then it’s a parallelogram (converse of a property).

What are the 6 ways to prove a quadrilateral is a parallelogram?

Well, we must show one of the six basic properties of parallelograms to be true!

  • 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)

What are the 5 characteristics of a parallelogram?

The parallelogram has the following properties:

  • Opposite sides are parallel by definition.
  • Opposite sides are congruent.
  • Opposite angles are congruent.
  • Consecutive angles are supplementary.
  • The diagonals bisect each other.


What 5 properties can be used to prove that a shape is a parallelogram?

Parallelograms have these identifying properties: Congruent opposite sides. Congruent opposite angles. Supplementary consecutive angles.

Is a quadrilateral a parallelogram yes or no?

Yes. A parallelogram is a quadrilateral with 2 pairs of parallel sides. The opposite sides on every rectangle are parallel, so every rectangle is a parallelogram.

How do you prove a quadrilateral is congruent?

Generally, you have to put sides an interior angles of one quadrilateral in correspondence with sides and angle of another and to prove that all corresponding pairs of sides and angles are congruent.

What makes a parallelogram?

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Which condition is not sufficient to prove that a quadrilateral is a parallelogram?

A quadrilateral is a parallelogram if a pair of opposite sides is parallel and congruent. A quadrilateral is a parallelogram if its diagonal bisect ecah other. A quadrilateral is a parallelogram if both pair of opposite angles are congruent. Consider the parallelogram in the given figure.

How do you prove a parallelogram is congruent?

Opposite angles of parallelograms are congruent. Adjacent angles of parallelograms are supplementary. Diagonals bisect each other. One pair of opposite sides is both parallel and congruent.

Do every quadrilateral is a parallelogram?

A rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals. On the other hand, not all quadrilaterals and parallelograms are rectangles. A rectangle has all the properties of a parallelogram, plus the following: The diagonals are congruent.

What are the attributes of a quadrilateral?

Quadrilateral just means “four sides”. (quad means four, lateral means side). A Quadrilateral has four-sides, it is 2-dimensional (a flat shape), closed (the lines join up), and has straight sides.

What quadrilateral has two parallel sides?

A quadrilateral with two sides parallel is called a trapezoid, whereas a quadrilateral with opposite pairs of sides parallel is called a parallelogram.

Are parallelogram quadrilateral with four right angles?

A rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals. On the other hand, not all quadrilaterals and parallelograms are rectangles.

Is a parallelogram like a square or a trapezoid?

Under the inclusive definition, all parallelograms (including rhombuses, rectangles and squares) are trapezoids. Rectangles have mirror symmetry on mid-edges; rhombuses have mirror symmetry on vertices, while squares have mirror symmetry on both mid-edges and vertices.