Quadrilateral

Definition

A quadrilateral is a four-sided polygon, where each side is a straight line segment and the opposite sides are parallel. Quadrilaterals are a fundamental shape in geometry and have various properties that are important in the context of topics like rectangles, triangles, and trapezoids.

5 Must Know Facts For Your Next Test

1. The sum of the interior angles of a quadrilateral is always 360 degrees.
2. Diagonals of a quadrilateral bisect each other in a parallelogram.
3. The diagonals of a rectangle are equal in length and perpendicular to each other.
4. The diagonals of a rhombus bisect each other at right angles and are equal in length.
5. Trapezoids have one pair of parallel sides, known as the bases, and the other two sides are non-parallel.

Review Questions

• Explain how the properties of a rectangle relate to the definition of a quadrilateral.
  • A rectangle is a special type of quadrilateral that has four right angles and two pairs of parallel sides that are equal in length. These properties of a rectangle, such as the perpendicular diagonals and equal opposite sides, are specific examples of the general characteristics of a quadrilateral. Understanding the defining features of a quadrilateral, like the parallel sides and straight line segments, helps to contextualize the unique properties of a rectangle within the broader category of four-sided polygons.
• Describe how the concept of a trapezoid relates to the definition of a quadrilateral.
  • A trapezoid is a quadrilateral that has one pair of parallel sides, known as the bases, and the other two sides are non-parallel. This specific configuration of parallel and non-parallel sides is an important variation within the broader class of quadrilaterals. Recognizing that a trapezoid is still a four-sided polygon with straight line segments demonstrates how the general definition of a quadrilateral encompasses the more specialized shape of a trapezoid and its unique properties.
• Analyze how the properties of a parallelogram connect to the overall definition and characteristics of a quadrilateral.
  • $$A\\ parallelogram\\ is\\ a\\ quadrilateral\\ with\\ two\\ pairs\\ of\\ parallel\\ sides\\ that\\ are\\ equal\\ in\\ length.\\ This\\ specific\\ arrangement\\ of\\ parallel\\ sides\\ is\\ a\\ key\\ feature\\ of\\ the\\ general\\ definition\\ of\\ a\\ quadrilateral,\\ which\\ states\\ that\\ a\\ quadrilateral\\ must\\ have\\ at\\ least\\ one\\ pair\\ of\\ parallel\\ sides.\\ The\\ fact\\ that\\ a\\ parallelogram's\\ diagonals\\ bisect\\ each\\ other\\ is\\ another\\ property\\ that\\ relates\\ to\\ the\\ overall\\ characteristics\\ of\\ quadrilaterals,\\ where\\ the\\ diagonals\\ of\\ any\\ four-sided\\ polygon\\ intersect\\ at\\ a\\ common\\ point.\\ Recognizing\\ these\\ connections\\ between\\ the\\ specific\\ properties\\ of\\ a\\ parallelogram\\ and\\ the\\ broader\\ definition\\ of\\ a\\ quadrilateral\\ is\\ crucial\\ for\\ understanding\\ the\\ relationships\\ between\\ different\\ types\\ of\\ four-sided\\ shapes.$$

Related terms

Parallelogram: A quadrilateral with two pairs of parallel sides, where the opposite sides are equal in length.

Rectangle:

A parallelogram with four right angles, where the opposite sides are equal in length.

Trapezoid:

A quadrilateral with one pair of parallel sides, known as the bases, and the other two sides are non-parallel.