Math - 2017-18

6.13 - Quadrilaterals

6.13    The student will describe and identify properties of quadrilaterals.

Bloom's Level:  Remember, Analyze

Adopted: 2009

BIG IDEAS

  • I can use the attributes of quadrilaterals to lay out a football or baseball field, create floor plans, and construct buildings through engineering and architecture.
  • I will develop analytical skills through comparing, contrasting, and sorting quadrilaterals by their attributes.


UNDERSTANDING THE STANDARD

  • A quadrilateral is a closed planar (two-dimensional) figure with four sides that are line segments.
  • A parallelogram is a quadrilateral whose opposite sides are parallel and opposite angles are congruent.
  • A rectangle is a parallelogram with four right angles.
  • Rectangles have special characteristics (such as diagonals are bisectors) that are true for any rectangle.
  • To bisect means to divide into two equal parts.
  • A square is a rectangle with four congruent sides or a rhombus with four right angles.
  • A rhombus is a parallelogram with four congruent sides.
  • A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases, and the nonparallel sides are called legs. If the legs have the same length, then the trapezoid is an isosceles trapezoid.
  • A kite is a quadrilateral with two pairs of adjacent congruent sides. One pair of opposite angles is congruent.
  • Quadrilaterals can be sorted according to common attributes, using a variety of materials.
  • Quadrilaterals can be classified by the number of parallel sides: a parallelogram, rectangle, rhombus, and square each have two pairs of parallel sides; a trapezoid has only one pair of parallel sides; other quadrilaterals have no parallel sides.
  • Quadrilaterals can be classified by the measures of their angles: a rectangle has four 90° angles; a trapezoid may have zero or two 90° angles.
  • Quadrilaterals can be classified by the number of congruent sides: a rhombus has four congruent sides; a square, which is a rhombus with four right angles, also has four congruent sides; a parallelogram and a rectangle each have two pairs of congruent sides.
  • A square is a special type of both a rectangle and a rhombus, which are special types of parallelograms, which are special types of quadrilaterals.
  • The sum of the measures of the angles of a quadrilateral is 360°.
  • A chart, graphic organizer, or Venn Diagram can be made to organize quadrilaterals according to attributes such as sides and/or angles.

ESSENTIALS

  • Can a figure belong to more than one subset of quadrilaterals?
    Any figure that has the attributes of more than one subset of quadrilaterals can belong to more than one subset. For example, rectangles have opposite sides of equal length. Squares have all 4 sides of equal length thereby meeting the attributes of both subsets. 

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

6.131  Sort and classify polygons as quadrilaterals, parallelograms rectangles, trapezoids, kites, rhombi, and squares based on their properties. Properties include number of parallel sides, angles measures, and number of congruent sides

6.132  Identify the sum of the measures of the angles of a quadrilateral as 360°.

KEY VOCABULARY

quadrilateral, 2-D figure, line segment, parallelogram, parallel, opposite angles, congruent, rectangle, right angle, diagonals, bisector, bisect, square, rhombus, trapezoid, base, non-parallel sides, legs, isosceles trapezoid, adjacent, common attributes, subsets, polygons, kites, rhombi, sum, Venn diagram

Updated: Jun 05, 2017