Q:
# What must one justify to prove that a quadrilateral ABCD is a parallelogram?

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### Quick Answer

Regents Prep explains that the quickest method for proving that a quadrilateral is a parallelogram is if one pair of opposite sides of the quadrilateral are both parallel and congruent. However, several other forms of proof exist as well.

Know MoreAccording to Wikipedia, in Euclidean geometry, a parallelogram is a simple quadrilateral, with four edges and four corners, characterized by its two pairs of parallel sides. Because of its parallel orientation, the opposite sides of a parallelogram are equal in length. The opposite angles of a parallelogram are also equal in measure. This congruence is proven by Euclid's parallel postulate, also known as Euclid's fifth postulate; it is part of Euclid's "Elements," which serves as the basis for the shortest method of proof previously described.

The basic definition of a parallelogram lends itself to several other methods of proof. For instance, one can prove that a quadrilateral is a parallelogram if the two pairs of opposite angles in the quadrilateral are congruent. Further, if the consecutive angles in the quadrilateral are supplementary, or equal to 180 degrees, then it is a parallelogram. Finally, one can also prove a quadrilateral is a parallelogram if the two diagonals of the quadrilateral can bisect each other, or divide each other equally in half.

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Q:
## Why is symmetry important?

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Full Answer >**Symmetry is important because it is the main feature of nature that restricts the permissible dynamic laws.**The concept of balance is very important to understanding how symmetry works.Filed Under: -
Q:
## How many quadrilaterals are there?

A:A quadrilateral is a four-sided polygon. There are many different possible shapes and variations a quadrilateral could take, but there are six main types according to the BBC.

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Q:
## Are intersecting lines always coplanar?

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Full Answer >**Two intersecting lines are always coplanar.**Each line exists in many planes, but the fact that the two intersect means they share at least one plane.Filed Under: -
Q:
## How many lines of symmetry does a star have?

A:The number of symmetry lines for a star depends on the particular types of star. A five-pointed star has five lines of symmetry. However, a six-pointed star has six lines of symmetry.

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