New Vocabulary parallelogram rhombus rectangle square kite trapezoid isosceles trapezoid

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1 6-. Plan bjectives To define and classif special tpes of quadrilaterals Eamples Classifing a Quadrilateral Classifing Coordinate Methods Using the Properties of Special Quadrilaterals 6- What You ll Learn To define and classif special tpes of quadrilaterals... And Wh To use the properties of special quadrilaterals with a kite, as in Eample Classifing Quadrilaterals Check Skills You ll Need G for Help Lesson -8 and page 65 Find the distance between the points to the nearest tenth..7. M(, -5), N(-7, ) 0.8. P(-, -), Q(-6, -9) 7.8. C(-, 6), (5, -) Find the slope of the line through each pair of points. 8. X(0, 6), Y(, 9) 5. R(, 8), S(6, 0) 6. A(, ), B(, ) New Vocabular parallelogram rhombus rectangle square kite trapezoid isosceles trapezoid Math Background The classification in this lesson categorizes quadrilaterals first b the number of pairs of parallel sides, and then shows their subsets. ther hierarchies are possible. More Math Background: p. 0C Lesson Planning and Resources See p. 0E for a list of the resources that support this lesson. Classifing Special Quadrilaterals Seven important tpes of quadrilaterals are defined below. Ke Concepts efinitions Special Quadrilaterals A parallelogram is a quadrilateral with both pairs of opposite sides parallel. A rhombus is a parallelogram with four congruent sides. PowerPoint Bell Ringer Practice Check Skills You ll Need For intervention, direct students to: Finding istance on the Coordinate Plane Lesson -8: Eample Etra Skills, Word Problems, Proof Practice, Ch. Slope Algebra Review, p. 65: Eample Real-World Connection A kite is not the onl special quadrilateral used to make a kite! 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 eactl one pair of parallel sides. The isosceles trapezoid at the right is a trapezoid whose nonparallel opposite sides are congruent. 06 Chapter 6 Quadrilaterals 06 Special Needs L Students ma assume that all quadrilaterals can be classified b one of the special names. raw eamples of quadrilaterals that cannot be given an more specific name than quadrilateral. learning stle: visual Below Level L Students can use geoboards to model the quadrilaterals in this lesson. learning stle: tactile

2 Classifing a Quadrilateral Judging b appearance, classif EFG in as man was as possible. EFG is a quadrilateral because it has four sides. G E F. Teach Guided Instruction It is a parallelogram because both pairs of opposite sides are parallel. Tactile Learners Quick Check It is a rectangle because it has four right angles. a. Judging b appearance, classif WXYZ at the right in as man was as possible. a b. See below left. b. Critical Thinking Which name gives the most information about WXYZ? Eplain. W X Z Y Use geoboards to model quadrilaterals. Connection to Coordinate Geometr The diagram below shows the relationships among special quadrilaterals. If necessar, displa the formulas for slope and distance. For: Quadrilateral Activit Use: Interactive Tetbook, 6- Kite No pairs of parallel sides Trapezoid Quadrilateral pair of parallel sides pairs of parallel sides Rectangle Parallelogram Rhombus PowerPoint Additional Eamples Judging b appearance, classif ABC in as man was as possible. A B a.wxyz is a quad. because it has sides; it is a ~ because both pairs of opp. sides are n; it is a rhombus because all sides are. b. rhombus, because that means it is a ~ and quad. with sides that are Vocabular Tip Although LMNP is a parallelogram, rhombus is the more precise name because it gives more information about the quadrilateral. Quick Check You can use what ou know about slope and distance to classif a quadrilateral. Isosceles Trapezoid Classifing b Coordinate Methods Square Coordinate Geometr etermine the most precise name for quadrilateral LMNP. Step Find the slope of each side. slope of = = LM M(, ) slope of = = L(, ) N(5, ) NP 5 P(, ) slope of MN = = 5 6 slope of LP = = Both pairs of opposite sides are parallel, so LMNP is a parallelogram. No sides are perpendicular, so LMNP is not a rectangle. Step Use the istance Formula to see if an pairs of sides are congruent. LM = Î ( ) ( ) = "5 MN = Î ( 5) ( ) = "5 NP = Î (5 ) ( ) = "5 LP = Î ( ) ( ) = "5 All sides are congruent, so LMNP is a rhombus. etermine the most precise name for quadrilateral ABC with vertices A(-, ), B(, ), C(, -), and (-, -). square quadrilateral, trapezoid etermine the most precise name for the quadrilateral with vertices Q(, ), B(, 9), H(8, 9), and A(0, ). isosceles trapezoid In parallelogram RSTU, m&r = - 0 and m&s = Find. 8 Resources ail Notetaking Guide 6- L ail Notetaking Guide 6- Adapted Instruction L Closure ABC is a square. Which classifications from this lesson also appl? Which do not appl? parallelogram, rectangle, rhombus; trapezoid, isosceles trapezoid, kite C Lesson 6- Classifing Quadrilaterals 07 Advanced Learners L Have students eplain wh the word eactl is necessar in the definition of a trapezoid. learning stle: verbal English Language Learners ELL Have students use magazines and newspapers to find real-world eamples for each special quadrilateral. Have students present their eamples speaking each name with correct pronunciation. learning stle: tactile 07

3 . Practice You can use the definitions of special quadrilaterals and algebra to find lengths of sides. Assignment Guide Using the Properties of Special Quadrilaterals A B -55 C Challenge Test Prep 60-6 Mied Review 65-7 Homework Quick Check To check students understanding of ke skills and concepts, go over Eercises,, 5, 5,. Auditor Learners Eercises 6 Have students work with partners to discuss the appearance of each quadrilateral to help reinforce the classifications and establish visual-verbal cues. Quick Check Algebra Find the values of the variables for the kite. KB = JB efinition of kite - 5 = = = 9 Substitute. Subtract from each side. Add 5 to each side. KT = + 6 = 5 Substitute 9 for. KT = JT efinition of kite 5 = + 5 Substitute. 0 = Subtract 5 from each side. 5 = ivide each side b. Find the values of the variables for the rhombus. Then find the lengths of the sides. a, b ; LN ST NT SL 5a L T 5 6 J K B b a 8 5 N Connection to Coordinate Geometr Eercise 6 Remind students that lines are perpendicular if the product of their slopes is -. Eercise 5 Before students begin, ask: What is the relationship between &F and &G? The are supplementar. Eample (page 07) b EXERCISES For more eercises, see Etra Skill, Word Problem, and Proof Practice. Practice and Problem Solving A G Practice b Eample for Help These quadrilaterals are made from a to building set. Judging b appearance, classif each quadrilateral in as man was as possible.. ~,.. rectangle, rhombus, square S T parallelogram trapezoid GPS Guided Problem Solving L Enrichment Reteaching Adapted Practice L L L Practice Name Class ate Practice 6- etermine the most precise name for each quadrilateral. L Classifing Quadrilaterals Eample (page 07) ~, rhombus kite trapezoid, isosc. trapezoid etermine the most precise name for each quadrilateral A (, ) B (7, ) E (, ) F (, ) 6 6 (, 0) C (5, 0) 0 H (, ) G (, ) Judging b appearance, classif each quadrilateral in as man was as possible rhombus 5 parallelogram 7 7 rhombus Chapter 6 Quadrilaterals Pearson Education, Inc. All rights reserved. Algebra Find the values of the variables. Then find the lengths of the sides of each quadrilateral. 9. rhombus ABC 0. parallelogram LNM. square FGHI A B m 8 N F f G 8 0 s 5m g 6 g 5 C L m M I 5f 8 H etermine the most precise name for each quadrilateral with the given vertices.. A(, ), B(, 5), C(6, ), (, 0). W(0, 5), X(, 5), Y(, ), Z(0, ). A(-, ), B(, 6), C(6, ), (, -) 5. P(-, 0), Q(-, ), R(, ), S(, ) 08

4 9., 9;,,, B Eample (page 08) Appl Your Skills Eercise kite isosc. trapezoid rectangle Coordinate Geometr Graph and label each quadrilateral with the given vertices. Then determine the most precise name for each quadrilateral. 8. See back of book.. A(, 5), B(7, 6), C(6, ), (, ). W(-, ), X(0, ), Y(, ), Z(0, -) 5. J(, ), K(5, ), L(7, ), M(, -) 6. R(-, -), S(, 0), T(, ), V(-, -) 7. N(-6, -), P(-, ), 8. E(-, ), F(-7, -), Q(0, ), R(-, 5) G(6, -), H(, ) Algebra Find the values of the variables. Then find the lengths of the sides. 9. kite 0. kite. kite B C A + -.8, 6; 6,.8;, 7, 7,.5,.5, 6.8, 6.8. isosceles trapezoid. rhombus. square ;,,, 7-9, 5; 5, ;,,, 5, 5, 5, 5 Algebra In each figure, find the measures of the angles and the lengths of the sides. 5. isosceles trapezoid EFG 6. rhombus HKJI 58, 58,, ; GPS (c - 0) K b - 6r 6, 6, 6, 6 E a F J a - 0, 0, 0, r + 0;,, b - c a + G 5, H r - I ( + 6) 7. Art American artist Charles emuth created M Egpt, the oil painting pictured at the left. It is in an art stle called Cubism, in which subjects are made of cubes and other geometric forms. Identif the tpes of special quadrilaterals ou see in the painting. rectangle, square, trapezoid 8. Multiple Choice K(-, 0), I(0, ), and T(, 0) are the vertices of a kite. Which point could be the fourth verte? E(0, ) E(0, 0) E(0, -) E(0, -0) raw each figure on graph paper. If not possible, eplain. 9. See margin. 9. a parallelogram that is neither 0. an isosceles trapezoid with vertical a rectangle nor a rhombus and horizontal congruent sides. a trapezoid with onl one right angle. a trapezoid with two right angles. a rhombus that is not a square. a kite with two right angles 5 iversit Eercise 7 Point out that artists have used representations of geometric figures for hundreds of ears. For eample, Arabian tiles show geometric shapes that tessellate. Ask students to describe other art forms that use geometric figures. Eercise 8 Encourage students to make a sketch to aid them in finding the fourth point. Then ask: What do ou know about the missing verte? It is opposite I, but it is not (0, ) which would form a rhombus. Error Prevention! Eercise As students describe a kite, make sure that the include the stipulation that opposite sides are not congruent. Point out that without that condition, squares and rhombuses would be considered kites. Tactile Learners Eercises 50 5 For each eercise, have students cut out cardboard triangles to connect in ever possible wa Lesson 6- Classifing Quadrilaterals Answers ma var. Samples are given Impossible; a trapezoid with one rt. l must have another, since two sides are n. 6 09

5 . Assess & Reteach PowerPoint Lesson Quiz G nline Homework Help Visit: PHSchool.com Web Code: aue Cop the Venn diagram. Add the labels Rectangles, Rhombuses, and Trapezoids to the diagram in the appropriate places. Quadrilaterals Parallelograms Judging b appearance, classif the quadrilaterals in Eercises and in as man was as possible... quadrilateral, kite quadrilateral, parallelogram, rectangle, rhombus, square. What is the most precise name for the figure in Eercise? kite. What is the most precise name for the figure in Eercise? square 5. Find the values of the variables in the rhombus below. A a 8 a a 60, 6, Alternative Assessment Have students work in pairs to identif eamples in the school building of four of the special quadrilaterals in Lesson 6- and then justif each classification. B C Real-World Connection To make this butterfl, an origami square was folded first on its diagonals.. A rhombus has sides, while a kite has pairs of adj. sides, but no opp. sides are. pp. sides of a rhombus are n, while opp. sides of a kite are not n. Problem Solving Hint In Eercises 50 5, if ou flip one of the two triangles, ou ma find different quadrilaterals. Rhombuses S Kites Squares d Rectangles d Trapezoids State whether each statement is true or false. Justif our response. You ma find the diagram from Eercise 5 helpful. 6. See margin. 6. All squares are rectangles. 7. A trapezoid is a parallelogram. 8. A rhombus can be a kite. 9. Some parallelograms are squares. 0. Ever quadrilateral is. All rhombuses are squares. a parallelogram.. Paper Folding Fold a nonsquare, rectangular piece of paper in half horizontall and then verticall, as shown at the right. raw and then cut along the line connecting the two opposite corners containing a fold. What quadrilateral do ou find when ou unfold the paper? Wh doesn t it matter what size rectangle ou start with? Rhombus; all sides are because the come from the same cut.. Identif a parallelogram, rhombus, rectangle, square, kite, and trapezoid in our classroom. State whether our trapezoid is isosceles. Check students work.. Writing escribe the difference between a rhombus and a kite. See left. Name each tpe of special quadrilateral that can meet the given condition. Make sketches to support our answers See margin. 5. eactl one pair of congruent sides 6. two pairs of parallel sides 7. four right angles 8. adjacent sides that are congruent 9. Error Analsis Lauren argues, A parallelogram has two pairs of parallel sides, so it certainl has one pair of parallel sides. Therefore a parallelogram must also be a trapezoid. What is the error in Lauren s argument? A trapezoid has onl one pair of n sides. Name the tpe(s) of special quadrilateral(s) it appears that ou can form b joining the triangles in each pair. Make sketches to support our answers. Sample two congruent scalene triangles Check students sketches. 50. rectangle, ~, kite parallelogram 5. rhombus, ~ 5. square, rhombus, ~ 5. rhombus, ~, kite 50. two congruent scalene right triangles 5. two congruent equilateral triangles 5. two congruent isosceles 5. two congruent isosceles right triangles acute triangles 0 Chapter 6 Quadrilaterals 6. True; a square is both a rectangle and a rhombus. 7. False; a trapezoid onl has one pair of n sides False; a kite does not have opp. sides. 9. True; all squares are?. 0. False; kites are not?.. False; onl rhombuses with rt. ' are squares Check students sketches. 5. some isos. trapezoids, some trapezoids 6. ~, rhombus, rectangle, square 7. rectangle, square 8. rhombus, square, kite, some trapezoids

6 C Challenge Identif a parallelogram, rhombus, rectangle, square, kite and trapezoid at each site. State whether our trapezoid is isosceles Check students work. 5. home 55. somewhere other than school and home Reasoning A scrap of paper covers part of each quadrilateral. Name all the special quadrilaterals that each could be. Eplain each choice See margin Test Prep Resources For additional practice with a variet of test item formats: Standardized Test Prep, p. 6 Test-Taking Strategies, p. 56 Test-Taking Strategies with Transparencies Test Prep G Multiple Choice Short Response Mied Review for Help Lesson 5-5 Lesson Which statement is NEVER true? C A. Square ABC is a rhombus. B. Parallelogram PQRS is a square. C. Trapezoid GHJK is a parallelogram.. Square WXYZ is a parallelogram. 6. Which statement is true for some, but not all, rectangles? J F. pposite sides are parallel. G. It is a parallelogram. H. Adjacent sides are perpendicular. J. All sides are congruent. 6. A parallelogram has four congruent sides. Which name best describes the figure? C A. trapezoid B. parallelogram C. rhombus. square 6. Which name best describes a parallelogram with four congruent angles? H F. kite G. rhombus H. rectangle J. square 6. A(-, ), B(-, -), and C(, ) are three vertices of quadrilateral ABC. Could ABC be a rectangle? Eplain. See margin. Can a triangle have sides with the given lengths? Eplain mm, 6 mm, mm ft, 0 ft, 7 ft 67. m, 5 m, 8 m See margin. No; 5 ± 7 w 0. No; ± 5 w 8. Quadrilaterals RSTV and NMQP are congruent. Find the length of the side or the measure of the angle Eplanations ma var. 56. ~, rectangle, trapezoid 57. ~, kite, rhombus, trapezoid, isos. trapezoid 58. kite, ~, rhombus, trapezoid, isos. trapezoid 59. ~, rectangle, square, rhombus, kite, trapezoid 6. [] Slope of AB is. The slope of BC is, so AB and BC are not. Since one l is not a right l and a rectangle requres all ' to be right ', the figure could not be a rectangle. [] incorrect slope R failure to recognize the information provided b the slopes 68. MN mm 69. VT mm R 70. ST 0 mm 7. &S 8 0 mm 7. &V &R 58 mm V S 0 T M 0 mm Q mm P 58 N Lesson Write an equation for the line parallel to =- - 5 that contains point (0, ). ± lesson quiz, PHSchool.com, Web Code: aua-060 Lesson 6- Classifing Quadrilaterals