6-1 Classifying Quadrilaterals

1 Classifying Quadrilaterals306 Chapter 6 QuadrilateralsLesson 1-8 and page 165 Find the distance between the points to the nearest (2,-5),N(-7, 1) (-1,-3),Q(-6,-9) (-4, 6),D(5,-3)Find the slope of the line through each pair of (0, 6),Y(4, 9) (3, 8),S(6, 0) (4, 3),B(2, 1) 1 New Vocabulary parallelogram rhombus rectangle square kite trapezoid isosceles trapezoid8334 What You ll Learn Todefine and classifyspecial types ofquadrilaterals.. And WhyTo use the properties ofspecial Quadrilaterals with akite, as in Example 3 Seven important types of Quadrilaterals are defined Special QuadrilateralsKey ConceptsDefinitionsSpecial QuadrilateralsAis a quadrilateral with both pairs of opposite sides a parallelogram with four congruent a parallelogram with four right a parallelogram with four congruent sides and four right a quadrilateral with two pairs of adjacent sides congruent and no opposite sides a quadrilateral with exactly one pair of parallel sides.

2 Theat the right is a trapezoid whose nonparallel opposite sides are trapezoidtrapezoidkitesquarerectanglerho mbusparallelogramConnectionReal-WorldA kite is not the onlyspecial quadrilateral used tomake a kite! Skills You ll NeedGOfor Help6-16-13061. PlanObjectives1To define and classify specialtypes of quadrilateralsExamples1 Classifying a Quadrilateral2 Classifying CoordinateMethods3 Using the Properties of SpecialQuadrilateralsMath BackgroundThe classification in this lessoncategorizes Quadrilaterals first by the number of pairs of parallelsides, and then shows their hierarchies are Math Background:p. 304 CLesson Planning andResourcesSee p. 304E for a list of theresources that support this Ringer PracticeCheck Skills You ll NeedFor intervention, direct students to:Finding Distance on theCoordinate PlaneLesson 1-8: Example 1 Extra Skills, Word Problems, ProofPractice, Ch.

3 1 SlopeAlgebra Review, p. 165: Example 1 PowerPointSpecial NeedsStudents may assume that all Quadrilaterals can beclassified by one of the special names. Draw examplesof Quadrilaterals that cannot be given any morespecific name than quadrilateral. Below LevelStudents can use geoboardsto model the Quadrilaterals in this style: visuallearning style: tactileLesson 6-1 Classifying Quadrilaterals307 Classifying a QuadrilateralJudging by appearance, classify DEFGin as many ways as a quadrilateral because it has four is a parallelogram because both pairs of opposite sides are is a rectangle because it has four right by appearance, classify WXYZat the rightin as many ways as ThinkingWhich name gives the most information about WXYZ? diagram below shows the relationships among special can use what you know about slope and distance to classify a by Coordinate MethodsCoordinate GeometryDetermine the most precise name for quadrilateral 1 Find the slope of each of ==slope of ==slope of ==slope of ==Both pairs of opposite sides are parallel, so LMNPis a sides are perpendicular, so LMNPis not a 2 Use the Distance Formula to see if any pairs of sides are sides are congruent, so LMNPis a the most precise name for quadrilateral ABCD with vertices A(-3, 3),B(2, 4),C(3,-1), and D(-2,-2).

4 Square22 Quick Check"5 (123)21(221)2"5 (523)21(221)2"5 (325)21(322)2"5 (321)21(322)22 12221123LP2 12322325MN12221523NP12322321 LMyxO24641L(1, 2)M(3, 3)P(3, 1)N(5, 2)EXAMPLEEXAMPLE22 WZYX11 Quick CheckEXAMPLEEXAMPLE11 DGEFKiteTrapezoidRectangleSquareRhombus2 pairs of parallel sides1 pair ofparallel sidesIsoscelesTrapezoidParallelogramNo pairs ofparallelsidesQuadrilaterala b. See below a quad. becauseit has 4 sides; it is a ~because both pairs ofopp. sides are n; it is arhombus because all 4sides are rhombus, because thatmeans it is a ~and quad. with 4 sides thatare OFor:Quadrilateral Activity Use:Interactive Textbook, 6-1 Although LMNPis aparallelogram, rhombusisthe more precisenamebecause it gives moreinformation about Tip3072. TeachGuided InstructionTactile LearnersUse geoboards to to CoordinateGeometryIf necessary, display the formulasfor slope and ExamplesJudging by appearance, classifyABCDin as many ways as , trapezoidDetermine the most precisename for the quadrilateral withvertices Q( 4, 4), B( 2, 9), H(8, 9),and A(10, 4).

5 Isosceles trapezoidIn parallelogram RSTU, m&R=2x-10 and m&S=3x+50. Find Daily Notetaking Guide 6-1 Daily Notetaking Guide 6-1 Adapted InstructionClosureABCDis a square. Whichclassifications from this lesson also apply?Which do notapply?parallelogram, rectangle,rhombus; trapezoid, isoscelestrapezoid, kiteL1L33322 DABC11 EXAMPLEEXAMPLE22 EXAMPLEEXAMPLE11 Advanced LearnersHave students explain why the word exactlyisnecessary in the definition of a Language LearnersELLHave students use magazines and newspapers to findreal-world examples for each special students present their examples speaking eachname with correct style: tactilelearning style: verbalPowerPoint308 Chapter 6 QuadrilateralsYou can use the definitions of special Quadrilaterals and algebra to find lengths of the Properties of Special QuadrilateralsAlgebraFind the values of the variables for the of kite3x-5=2x+ 2xfrom each 5 to each +6=15 Substitute 9 for of kite15=2y+ 5 from each each side by the values of the variables for the rhombus.

6 Then find the lengths of the Quadrilaterals are made from a toy building set. Judging by appearance,classify each quadrilateral in as many ways as the most precise name for each 2(page 307)Example 1(page 307)5a 43a 83b 24b 2 NLST33 Quick CheckEXAMPLEEXAMPLE333x 52x 42y 5x 6 BTJKP ractice and problem SolvingFor more exercises, see Extra Skill, Word problem , and Proof by ExampleAAa 2, b 4; LN ST NT SL 14~, rectangle, rhombus, squareparallelogramtrapezoid~, rhombuskiterhombusrhombusparallelogramtr apezoid, isosc. trapezoidGOforHelp3. PracticeAssignment GuideAB1-55 CChallenge56-59 Test Prep60-64 Mixed Review65-74 Homework Quick CheckTo check students understandingof key skills and concepts, go overExercises 13, 21, 25, 35, LearnersExercises 1 6 Have students work with partners to discuss theappearance of each quadrilateralto help reinforce the classificationsand establish visual-verbal to CoordinateGeometryExercise 16 Remind students thatlines are perpendicular if theproduct of their slopes is 25 Before students begin,ask: What is the relationshipbetween &Fand &G?

7 They problem SolvingGPSE nrichmentReteachingAdapted PracticeNameClassDatePractice 6-1 Classifying QuadrilateralsDetermine the most precise name for each by appearance, classify each quadrilateral in as many ways as the values of the variables. Then find the lengths of the sides ofeach the most precise name for each quadrilateral with the (1, 4),B(3, 5),C(6, 1),D(4, 0) (0, 5),X(3, 5),Y(3, 1),Z(0, 1) (-2, 4),B(2, 6),C(6, 4),D(2,-3) (-1, 0),Q(-1, 3),R(2, 4),S(2, 1)3f 22g 5g 65f 8 FGIH2m 85m 2s 13m 1 ONLM2x 33x 1018 xx 4 ABCD42 4 6 4246yxOE ( 2, 3)F (1, 3)H ( 2, 2)G (1, 2)4210yxOA(3, 3)B(7, 3)D(1, 0)C(5, 0) Pearson Education, Inc. All rights 6-1 Classifying GeometryGraph and label each quadrilateral with the given determine the most precise name for each (3, 5),B(7, 6),C(6, 2),D(2, 1) (-1, 1) ,X(0, 2),Y(1, 1),Z(0,-2) (2, 1),K(5, 4),L(7, 2),M(2,-3) (-2,-3),S(4, 0),T(3, 2),V(-3,-1) (-6,-4),P(-3, 1), (-3, 1),F(-7,-3),Q(0, 2),R(-3, 5)G(6,-3),H(2, 1)AlgebraFind the values of the variables.

8 Then find the lengths of the each figure, find the measures of the angles and the lengths of the trapezoid artist Charles Demuth created My Egypt, the oil paintingpictured at the left. It is in an art style called Cubism, in which subjects aremade of cubes and other geometric the types of specialquadrilaterals you see in the , square, ChoiceK(-3, 0),I(0, 2), and T(3, 0) are the vertices of a kite. Whichpoint could be the fourth vertex? DE(0, 2)E(0, 0)E(0,-2)E(0,-10)Draw each figure on graph paper. If not possible, 34. See parallelogram that is neither isosceles trapezoid with verticala rectangle nor a rhombusand horizontal congruent trapezoid with only one right trapezoid with two right rhombus that is not a kite with two right angles 4b - 6r2r - 4r + 1b - 3 KJHI(2x + 6) x a - 4a2a + 211 EFGD(4c - 20) c x2x2 Apply Your SkillsBB2x - 73y - 9y - 12y - 5155x3y4x + 32x + 24x + 32x4y + 1x2y - 53x - 4x + + 22y - - 12x 2y 6 BCDA13x2x2 Example 3(page 308)Exercise 27rectanglekite13 18.

9 See backof 11, y 29; 13, 13, 23, 23x 4, y ; , , , 5, y 4; 3, 3, 3, 3x 2, y 6; 2, 7, 7, 2x 1; 4, 2, 4, 7x 3, y 5; 15, 15, 15, 1540, 40, 140, 140; 11, 11, 15, 3258, 58, 122, 122; 6, 6, 6, 6isosc. trapezoidGPSD iversityExercise 27 Point out that artistshave used representations ofgeometric figures for hundreds of years. For example, Arabiantiles show geometric shapes thattessellate. Ask students to describeother art forms that use 28 Encourage studentsto make a sketch to aid them infinding the fourth point. Thenask: What do you know about themissing vertex? It is opposite I,but it is not (0, 2) which wouldform a Prevention!Exercise 44As students describe a kite, make sure that they includethe stipulation that opposite sidesare not congruent. Point out thatwithout that condition, squaresand rhombuses would beconsidered LearnersExercises 50 53 For each exercise,have students cut out cardboardtriangles to connect in everypossible 34.

10 Answers may are Impossible; a trapezoidwith one rt. lmusthave another, sincetwo sides are the Venn diagram. Add the labels Rectangles, Rhombuses,and Trapezoidsto the diagram in the appropriate whether each statement is trueor your response. You may findthe diagram from Exercise 35 41. See squares are trapezoid is a rhombus can be a parallelograms are quadrilateral is rhombuses are FoldingFold a nonsquare, rectangularpiece of paper in half horizontally and thenvertically, as shown at the right. Draw andthen cut along the line connecting the two opposite corners containing a fold. What quadrilateral do you find when you unfold the paper? Why doesn t it matter what size rectangle you start with? a parallelogram, rhombus, rectangle, square, kite, and trapezoid in yourclassroom. State whether your trapezoid is students the difference between a rhombus and a each type of special quadrilateral that can meet the given condition.