7.4 Quadrilaterals

7.4QuadrilateralsHow can you classify quadrilaterals?Quad means four and lateralmeans side. So, quadrilateral meansa polygon with four sides.1QuadrilateralsACTIVITY: Using Descriptions to Form QuadrilateralsWork with a partner. Use a geoboard to form a quadrilateral that fits the givendescription. Record your results on geoboard dot paper.a. Form a quadrilateral with exactly one pair of parallel sides.The top andbottom sidesare parallel.b. Form a quadrilateral with four congruent sides and four right angles.c. Form a quadrilateral with four right angles that is not a square.GeometryIn this lesson, you will understand that the sum ofthe angle measures of anyquadrilateral is 360 . find missing anglemeasures inquadrilaterals. constructquadrilaterals.2d. Form a quadrilateral with four congruent sides that is not a square.e. Form a quadrilateral with two pairs of congruent adjacent sides andwhose opposite sides are not congruent.f.Form a quadrilateral with congruent and parallel opposite sides thatis not a rectangle.ACTIVITY: Naming QuadrilateralsWork with a partner. Match the names square, rectangle, rhombus,parallelogram, trapezoid, and kite with your 6 drawings in Activity 1.292Chapter 7ms red pe 0704.indd 292Constructions and Scale Drawings2/2/15 8:26:59 AM

3ACTIVITY: Forming QuadrilateralsWork with a partner. Form each quadrilateral on your geoboard. Then moveonly one vertex to create the new type of quadrilateral. Record your resultson geoboard dot paper.a. Trapezoid4MathPracticeUse Technologyto ExploreHow does geometrysoftware help youlearn about thecharacteristics ofa quadrilateral?Kiteb. KiteRhombus (not a square)ACTIVITY: Using Technology to Draw QuadrilateralsWork with a partner. Use geometry software to draw a quadrilateral that fitsthe given description.a. a square with a side length of 3 unitsb. a rectangle with a width of 2 units anda length of 5 unitsc. a parallelogram with side lengths of6 units and 1 unitd. a rhombus with a side length of4 unitsABegin by drawingtwo sides thatform a right angle.390îB3C5. REASONING Measure the angles of each quadrilateral you formedin Activity 1. Record your results in a table. Include the sum of theangle measures. Then describe the pattern in the table and write aconclusion based on the pattern.6. IN YOUR OWN WORDS How can you classify quadrilaterals? Explainusing properties of sides and angles.Use what you learned about quadrilaterals to completeExercises 4 –6 on page 296.Section 7.4ms red pe 0704.indd 293Quadrilaterals2932/2/15 8:27:09 AM

Lesson7.4Lesson TutorialsA quadrilateral is a polygon with four sides. The diagram shows propertiesof different types of quadrilaterals and how they are related. Whenidentifying a quadrilateral, use the name that is most specific.Key Vocabularykite, p. 294QuadrilateralReadingRed arrows indicateparallel sides.TrapezoidParallelogramquadrilateral withexactly one pair ofparallel sidesquadrilateral withopposite sides that areparallel and congruentKitequadrilateral with two pairsof congruent adjacent sides andopposite sides that are not congruentRhombusRectangleparallelogram withfour right anglesparallelogram withfour congruent sidesSquareparallelogram with four congruentsides and four right anglesEXAMPLEClassifying Quadrilaterals1Classify the quadrilateral.Study Tipb.a.In Example 1(a), thesquare is also aparallelogram, arectangle, and arhombus. Square is themost specific name.The quadrilateral hasfour congruent sidesand four right angles.The quadrilateral has two pairs ofcongruent adjacent sides andopposite sides that are not congruent.So, the quadrilateralis a square.So, the quadrilateral is a kite.Classify the quadrilateral.Exercises 4 – 9294Chapter 7ms red pe 0704.indd 2941.2.3.Constructions and Scale Drawings2/2/15 8:27:20 AM

Sum of the Angle Measures of a QuadrilateralWordsThe sum of the angle measuresof a quadrilateral is 360 .Algebra2EXAMPLE115í70ízíwíyíw x y z 360xíFinding an Angle Measure of a QuadrilateralFind the value of x.xí70 75 115 x 360Write an equation.260 x 360Combine like terms.75í 260 260x Subtraction Property of Equality100Simplify.The value of x is 100.EXAMPLE3Constructing a QuadrilateralDraw a parallelogram with a 60 angle and a 120 angle.Step 1: Draw a line.90 10 0401400 10180 170 1 20 360 0150 1 40120í60í0 1800Step 3: Draw the remaining side. Make surethat both pairs of opposite sides areparallel and congruent.90 10 017160 10015 200 3014 0460í8070 10 0 90 80 110 170260 0 11060 0 13250 0 150 0130 18000 10180 170 1 20 360 0150 408070 10 0 90 80 110 170260 0 11060 0 13250 0 150 01317160 10015 200 3014 04Step 2: Draw a 60 angleand a 120 anglethat each haveone side onthe line.120íFind the value of x.Exercises 10–12and 14–174.100íxí80í5.xí81í100í124í6. Draw a right trapezoid whose parallel sides have lengthsof 3 centimeters and 5 centimeters.Section 7.4ms red pe 0704.indd 295Quadrilaterals2952/2/15 8:27:27 AM

Exercises7.4Help with Homework1. VOCABULARY Which statements are true?a. All squares are rectangles.b. All squares are parallelograms.c. All rectangles are parallelograms.d. All squares are rhombuses.e. All rhombuses are parallelograms.2. REASONING Name two types of quadrilaterals with four right angles.3. WHICH ONE DOESN’T BELONG? Which type of quadrilateraldoes not belong with the other three? Explain your reasoning.rectanglesquareparallelogramkite6) 39 (- 3) 3 (- 9) 4 (- 1)9 (-Classify the quadrilateral.14.5.6.7.8.9.Find the value of x.2 22í13. KITE MAKING What is themeasure of the angle atthe tail end of the kite?296Chapter 7ms red pe 0704.indd 296Constructions and Scale Drawings2/2/15 8:27:30 AM

Draw a quadrilateral with the given description.3 14. a trapezoid with a pair of congruent, nonparallel sides15. a rhombus with 3-centimeter sides and two 100 angles16. a parallelogram with a 45 angle and a 135 angle17. a parallelogram with a 75 angle and a 4-centimeter sideCopy and complete using always, sometimes, or never.?18. A square is?19. A square isa rectangle.a rhombus.20. A rhombus is?a square.21. A parallelogram is22. A trapezoid is?a kite.23. A rhombus is?a trapezoid.a rectangle.24. DOOR The dashed line shows how you cut thebottom of a rectangular door so it opens more easily.a. Identify the new shape of the door. Explain.b. What is the new angle at the bottom left sideof the door? Explain.91.5íQuadrilaterals?Trapezoids?26.?25. VENN DIAGRAM The diagram showsthat some quadrilaterals are trapezoids,and all trapezoids are quadrilaterals.Copy the diagram. Fill in the namesof the types of quadrilaterals to showtheir relationships.Consider the parallelogram.55íxía. Find the values of x and y.125íb. Make a conjecture about opposite anglesin a parallelogram.yíc. In polygons, consecutive interior angles share a common side. Make aconjecture about consecutive interior angles in a parallelogram.Write the ratio as a fraction in simplest form. (Section 5.1)27. 3 turnovers : 12 assists28. 18 girls to 27 boys29. 42 pens : 35 pencils30. MULTIPLE CHOICE Computer sales decreased from 40 to 32. What is thepercent of decrease? (Section 6.5)A 8% B 20% C 25% Section 7.4ms red pe 0704.indd 297D 80% Quadrilaterals2972/2/15 8:27:37 AM

Form a quadrilateral with exactly one pair of parallel sides. b. Form a quadrilateral with four congruent sides and four right angles. c. Form a quadrilateral with four right angles that is not a square. d. Form a quadrilateral with four congruent sides that is not a square. e. Form a quadrilateral with two pairs of congruent adjacent sides and