Question

The definition of a parallelogram says, "If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram" Quadrilateral LNDA has both pairs of opposite sides parallel. What conclusion can you make? What type of reasoning did you use?

Name: Problem 6, Chapter 2: Discovering Geometry an Investigative Approach
Uploaded: 2021-08-07T18:48:45-08:00
Duration: 55 s
Channel: Jay Patel
Description: The definition of a parallelogram says, "If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram" Quadrilateral LNDA has both pairs of opposite sides parallel. What conclusion can you make? What type of reasoning did you use?

   The definition of a parallelogram says, "If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram" Quadrilateral LNDA has both pairs of opposite sides parallel. What conclusion can you make? What type of reasoning did you use?

Discovering Geometry an Investigative Approach

Michael Serra 4th Edition

Chapter 2, Problem 6

Instant Answer

Solved by Expert Jay Patel

08/07/2021

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A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Show more…

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The definition of a parallelogram says, "If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram" Quadrilateral LNDA has both pairs of opposite sides parallel. What conclusion can you make? What type of reasoning did you use?

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Key Concepts

Parallelogram Definition

This core concept states that if a quadrilateral has both pairs of opposite sides parallel, then it qualifies as a parallelogram. Understanding this definition is crucial in geometry because it allows one to categorize shapes based on properties derived from parallelism, making it a fundamental tool in proving characteristics of quadrilaterals.

Deductive Reasoning

Deductive reasoning is the process of drawing a specific conclusion based on a general principle or rule. In this context, the general definition of a parallelogram is applied to a specific quadrilateral (LNDA) to conclude that it is indeed a parallelogram, demonstrating the use of logical steps to arrive at a valid and certain conclusion.

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