#### 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**

6.13_{1} **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

_{2}

**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*