8.2 Quadrilaterals
EnglishSpanishQuadrilaterals8.2How can you classify quadrilaterals?STANDARDSTAANDARDSOF LEARNING6.13“Quad” means four and “lateral”means side. So, quadrilateral meansa polygon with four sides.1QuadrilateralsACTIVITY: Using Descriptions to Draw QuadrilateralsWork with a partner. Use a geoboard to form a quadrilateral that fits the givendescription. Record your results on geoboard dot paper.Sample: 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.d. 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.2Form 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 1.344Chapter 8Geometry
EnglishSpanish3ACTIVITY: 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. TrapezoidKiteb. KiteRhombus (not a square)Inductive Reasoning4. Work with a partner. Measure the angles of each quadrilateral youformed in Activity 1. Record your results in the table. 1 2 3 4 1 2 3 4a.b.c.d.e.f.5. Describe the pattern in the table. Write a conclusion based onthe pattern.6. IN YOUR OWN WORDS How can you classify quadrilaterals? Explain usingproperties of sides and angles.Use what you learned about quadrilaterals to completeExercises 4 –6 on page 348.Section 8.2Quadrilaterals345
English8.2SpanishLessonLesson 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. 346QuadrilateralReadingRed 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 anglesEXAMPLEIdentifying Quadrilaterals1Identify the quadrilateral.Study Tipb.a.In Example 1a, thesquare is also aparallelogram, arectangle, and arhombus. Square is themost specific name.The quadrilateral hasfour congruent sides andfour right angles. So, it isa square.The quadrilateral has two pairsof congruent adjacent sidesand opposite sides that are notcongruent. So, it is a kite.Identify the quadrilateral.Exercises 4 – 9346Chapter 81.Geometry2.3.
EnglishSpanishSum of the Angle Measures of a QuadrilateralWordsAlgebraEXAMPLE115í2The sum of the angle measuresof a quadrilateral is 360 .yíw x y z 360xíFinding an Angle Measure of a QuadrilateralFind the value of x.xí70 75 115 x 36070ízíwíWrite an equation.260 x 36075í 260Combine like terms. 260Subtract 260 from each side.x 100Simplify.The value of x is 100.EXAMPLEReading3Real-Life ApplicationYou cut a wooden block to make a CO2racecar. The top right angle of the blockis 105 . What is the measure of the topleft angle?CO2 is an abbreviatedway to refer to carbondioxide.90 90 105 x 360 285Combine like terms. 285Subtract 285 from each side.x 75carbon dioxide105íWrite an equation.285 x 360CO2xíSimplify.The measure of the top left angle is 75 .Find the value of x.Exercises 10–124.120íxí60í5.xí81í120í124í6. WHAT IF? In Example 3, the measure of the top rightangle is 100 . What is the measure of the top left angle?Section 8.2Quadrilaterals347
EnglishSpanishExercises8.2Help 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 (-Identify the quadrilateral.14.5.6.7.8.9.Find the value of x.2 13.348Chapter 8GeometryKITE MAKING You make the kite shown. To checkyour plans, you measure the angle at the tail end ofthe kite. What should the measure of this angle be?52í
EnglishSpanish14. MAGNETS Draw a diagram of how to form eachquadrilateral using the bars and spheres shown.a. Trapezoidb. Rhombusc. ParallelogramCopy and complete using always, sometimes, or never.?15. A square isa rectangle.16. A square is?a rhombus.17. A rhombus is?a square.18. A parallelogram is19. A trapezoid is?a kite.20. A rhombus is?a trapezoid.a rectangle.21. 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?23.?22. VENN DIAGRAM The diagram showsthat some quadrilaterals are trapezoidsand all trapezoids are quadrilaterals.Copy the diagram. Fill in the namesof the types of quadrilaterals to showtheir relationships.You share a rectangular bedroom that is 20 feet long and10 feet wide with your sibling. You want to divide the room into twocongruent figures.a. Draw diagrams showing three possible types of congruent figuresyou can use.b. Which design do you like the most? the least? Explain.Decide whether the rates are equivalent. (Section6.2)SECTION6.248 blinks 80 blinks3 minutes 5 minutes24 airplanes 16 airplanes3 hours2 hours24. —, —25. —, —26. MULTIPLE CHOICE Your school spent 539.40 to buy dictionaries at 8.99 each. Whichis the best estimate of how many dictionaries were purchased? (SectionSECTION4.1)4.1A 40 B 50 C 60 Section 8.2D 70 Quadrilaterals349
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
special quadrilaterals. Categorize quadrilaterals based upon their properties. Make conjectures about the midsegments of quadrilaterals. Understand that the vertices of cyclic quadrilaterals lie on the same circle. You have classifi ed
Identify Special Quadrilaterals Objective: Students will be able to identify special quadrilaterals using specific properties. Agenda Special Quadrilaterals –Chart Properties Special Quadrilaterals –Identify
What everyday objects are quadrilaterals? (Answers will vary. Possible answers: sheet of paper, street signs, etc.) Using the Digital Lesson Show students different flat figures with cutouts or drawings. Have them identify the quadrilaterals and describe the differences between the quadrilaterals and the other figures. Learning Task
TIPS4RM: Grade 8: Unit 4 – Lines, Angles, Triangles, and Quadrilaterals 5 4.1.2: From Diagonals to Quadrilaterals Grade 8 1. Explore all of the ways that you can position two intersecting paper strips or geo-strips. 2. For each shape that you make, mark a point in the four
Investigating Quadrilaterals Part 2 1. Download the file 2.5 Investigating Quadrilaterals.gsp from My Resources Grade 9 Academic Mathematics Unit 2: Geometry section of the course website. 2. Using the tabs on the bottom of the screen, investigate the 6 quadrilaterals by measuring the side lengths and anlges of the interior (smaller) quadrilateral.
properties of quadrilaterals. Related SOL: 3.12b, 3.13, 4.10b, 5.13a Learning Intentions Content – I am learning about the relationship between the properties of shapes and quadrilaterals. Language – I am learning to describe and write ab
Name and classify quadrilaterals according to their properties. Identify the minimal information required to define a quadrilateral. Sketch quadrilaterals with given conditions. COMMON CORE STATE STANDARDS This lesson relates to the following Standards for Mathematical Co
Quadrilaterals and Their Diagonals Distribute worksheet on the opposite page, angle rulers or protractors, and rulers. Have the participants complete in groups. Each drawing is the beginning of a quadrilateral. Participants are to finish each shape as labeled. This is a review of common quadrilaterals and
