What makes a parallelogram a quadrilateral

Some textbooks say a kite has at least two pairs of adjacent congruent sides, so a rhombus is a special case of a kite. A scalene quadrilateral is a four-sided polygon that has no congruent sides. Three examples are shown below. The following Venn Diagram shows the inclusions and intersections of the various types of quadrilaterals. Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC. Media outlet trademarks are owned by the respective media outlets and are not affiliated with Varsity Tutors.

Varsity Tutors connects learners with experts. Instructors are independent contractors who tailor their services to each client, using their own style, methods and materials. Quadrilaterals: Classification A quadrilateral is a polygon with four sides.

There are many special types of quadrilateral. B are supplementary angles. Usually the transversal has been AC, but this time you'll use AB. Because your two angles on the same side of the transversal are supplementary, Theorem A similar argument shows that AB? Ah, the last name game of this series! If you have a quadrilateral that has diagonals that bisect each other, your quadrilateral is a parallelogram.

If you look at Figure You will make use of Theorem The two diagonals divide the parallelogram into four triangles. Because vertical angles are congruent, you can use the SAS Postulate to show that? BMC and? All rights reserved including the right of reproduction in whole or in part in any form. To order this book direct from the publisher, visit the Penguin USA website or call You can also purchase this book at Amazon.

When Is a Parallelogram a Rectangle? When Is a Parallelogram a Rhombus? When Is a Parallelogram a Square? C and? See also:. Geometry: Properties of Parallelograms. Trending Here are the facts and trivia that people are buzzing about. Is Vatican City a Country? The Languages of Africa.

You can prove this with either a two-column proof or a paragraph proof. We can use one of these ways in a two-column proof.

Bear in mind that, to challenge you, most problems involving parallelograms and proofs will not give you all the information about the presented shape. Here, for example, you are given a quadrilateral and told that its opposite sides are congruent.

Theorem: If a transversal cuts across two lines and the alternate interior angles are congruent, then the lines are parallel. The two-column proof proved the quadrilateral is a parallelogram by proving opposite sides were parallel. Paragraph Proof You can also use the paragraph proof form for any of the six ways. Paragraph proofs are harder to write because you may skip a step or leave out an explanation for one of your statements.

You may wish to work very slowly to avoid problems. Always start by making a drawing so you know exactly what you are saying about the quadrilateral as you prove it is a parallelogram. Here is a proof still using opposite sides parallel, but with a different set of given facts.

You are given a quadrilateral with diagonals that are identified as bisecting each other. They are congruent because they are vertical angles opposite angles sharing a vertex point. Notice that we have two sides and an angle of both triangles inside the quadrilateral.

Those two angles are alternate interior angles, and if they are congruent, then sides FI and SH are parallel. You can repeat the steps to prove FH and IS parallel, which means two pairs of opposite sides are parallel.

Thus, you have a parallelogram. In both proofs, you may say that you already were given a fact that is one of the properties of parallelograms. That is true with both proofs, but in neither case was the given information mathematically proven.