Chapter 6 Lesson 1Chapter 6 Lesson 1

Objective:Objective: To define and To define and classify special types of classify special types of

quadrilaterals.quadrilaterals.

Classifying Special Classifying Special QuadrilateralsQuadrilaterals

Definitions:Definitions:  A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Consecutive angles are supplementary.

A rhombus is a parallelogram with four congruent sides.

A rectangle is a parallelogram with four right angles.

A square is a parallelogram with four congruent sides and four right angles.

A kite is a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent.

                                                

 A trapezoid is a quadrilateral with exactly one pair of parallel sides. The isosceles trapezoid at the right is a trapezoid whose nonparallel opposite sides are congruent.

Example 1: Example 1: Classifying Classifying QuadrilateralsQuadrilaterals

Judging by appearance, classify DEFG in as many ways as possible.

DEFGDEFG is a quadrilateral because it has four sides. is a quadrilateral because it has four sides. It is a parallelogram because both pairs of opposite It is a parallelogram because both pairs of opposite

sides are parallel. sides are parallel. It is a rectangle because it has four right angles.It is a rectangle because it has four right angles.

Example 2: Example 2: Classifying Classifying QuadrilateralsQuadrilaterals

Judging by appearance, classify ABCD Judging by appearance, classify ABCD in as many ways as possible.in as many ways as possible.

AA

BB

DD

CC

Quadrilateral

Trapezoid

Special QuadrilateralsSpecial Quadrilaterals

Example 3: Example 3: Classifying by Coordinate Classifying by Coordinate MethodsMethods

Determine the most precise name for quadrilateral LMNP.

Step 1: Find the slope of each line.

• Slope of LM =

•Slope of NP =

•Slope of MN =

•Slope of LP =

21

1323

21

3512

21

5323

21

3112

12

12

xx

yy

Slope FormulaSlope Formula

Example 3: (cont.)Example 3: (cont.)Both pairs of opposite sides are parallel, so LMNP is a parallelogram. No sides are perpendicular, so

LMNP is not a rectangle.

Step 2: Use the distance formula

212

212 yyxxd

All sides are congruent, so LMNP is a All sides are congruent, so LMNP is a rhombus.rhombus.

Example 4: Example 4: Using the Properties of Special Using the Properties of Special

QuadrilateralsQuadrilaterals

Find the values of the variables for the Find the values of the variables for the kite. kite.

                                                                                                                     

                                                                                                                                                                                                                                                                

                                                                         

Example 5: Example 5: Using the Properties of Special Using the Properties of Special

QuadrilateralsQuadrilaterals

Find the values of the variables for the Find the values of the variables for the rhombus. Then find the lengths of the rhombus. Then find the lengths of the

sides. sides.                                                                                                                      

                                                                                                                                                                                                                                                                

                                                                         

5a + 4

3b + 2

3a + 8

4b - 2S

L

T

N2423 bb4b

8345 aa2a

14 SLNTSTLN

AssignmentAssignment

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