Chapter 4 Resource Masters - Math Class

1 Chapter 4 Resource MastersGeometryReading to Learn MathematicsVocabulary BuilderNAME _____ DATE _____ PERIOD _____44 Glencoe/McGraw-HillviiGlencoe GeometryVocabulary BuilderThis is an alphabetical list of the key vocabulary terms you will learn in Chapter you study the Chapter , complete each term s definition or description. Rememberto add the page number where you found the term. Add these pages to yourGeometry Study Notebook to review vocabulary at the end of the TermFound on PageDefinition/Description/Exampleacute trianglebase anglescongruence transformationkuhn GROO uhnscongruent trianglescoordinate proofcorollaryequiangular triangleequilateral triangleexterior angle(continued on the next page) Glencoe/McGraw-HillviiiGlencoe GeometryVocabulary TermFound on PageDefinition/Description/Exampleflow proofincluded angleincluded sideisosceles triangleobtuse triangleremote interior anglesright trianglescalene triangleSKAY leenvertex angle Reading to Learn MathematicsVocabulary Builder(continued)

2 NAME _____ DATE _____ PERIOD _____44 Learning to Read MathematicsProof BuilderNAME _____ DATE _____ PERIOD _____44 Glencoe/McGraw-HillixGlencoe GeometryProof BuilderThis is a list of key theorems and postulates you will learn in Chapter 4. As youstudy the Chapter , write each theorem or postulate in your own words. Includeillustrations as appropriate. Remember to include the page number where youfound the theorem or postulate. Add this page to your geometry Study Notebookso you can review the theorems and postulates at the end of the or PostulateFound on PageDescription/Illustration/Abbreviatio nTheorem Sum TheoremTheorem Angle TheoremTheorem Angle TheoremTheorem Congruence (AAS)Theorem Congruence (LL)Theorem Congruence (HA)(continued on the next page) Glencoe/McGraw-HillxGlencoe GeometryTheorem or PostulateFound on PageDescription/Illustration/Abbreviatio nTheorem Congruence (LA)Theorem Triangle TheoremTheorem Congruence (SSS)Postulate Congruence (SAS)Postulate Congruence (ASA)Postulate Congruence(HL)

3 Learning to Read MathematicsProof Builder(continued)NAME _____ DATE _____ PERIOD _____44 Study Guide and InterventionClassifying TrianglesNAME _____ DATE _____ PERIOD _____4-14-1 Glencoe/McGraw-Hill183 Glencoe GeometryLesson 4-1 Classify Triangles by AnglesOne way to classify a triangle is by the measures of its angles. If oneof the angles of a triangle is an obtuse angle, then the triangle is an obtuse triangle. If oneof the angles of a triangle is a right angle, then the triangle is a right triangle. If all threeof the angles of a triangle are acute angles, then the triangle is an acute triangle. If all three angles of an acute triangle are congruent, then the triangle is an equiangular each three angles are congruent, so all three angles have measure 60.

4 The triangle is an equiangular triangle has one angle that is obtuse. It is an obtuse triangle has one right angle. It is a right each triangle as acute,equiangular,obtuse,or !28!92!FDB45!45!90!XYW65!65!50!UVT60!60! 60!QRS120!30!30!NOP67!90!23!KLM90!60!30! GHJ25!35!120!DFE60!ABCE xampleExampleExercisesExercises Glencoe/McGraw-Hill184 Glencoe GeometryClassify Triangles by SidesYou can classify a triangle by the measures of its numbers of hash marks indicate congruent sides. If all threesides of a triangle are congruent, then the triangle is an equilateral triangle. If at least twosides of a triangle are congruent, then the triangle is an isosceles triangle.

5 If no twosides of a triangle are congruent, then the triangle is a scalene each sides are three sides are The triangle has no pairThe triangle is an congruent. The triangle of congruent sides. It is isosceles an equilateral scalene each triangle as equilateral,isosceles,or the measure of each side of equilateral !RSTwith RS!2x"2,ST!3x,and TR!5x# the measure of each side of isosceles !ABCwith AB!BCif AB!4y,BC!3y"2, and AC! the measure of each side of !ABCwith vertices A(#1, 5),B(6, 1), and C(2,#6).Classify the !"GCA231215 XVTNRPLJHS tudy Guide and Intervention (continued)Classifying TrianglesNAME _____ DATE _____ PERIOD _____4-14-1 ExampleExampleExercisesExercisesSkills PracticeClassifying TrianglesNAME _____ DATE _____ PERIOD _____4-14-1 Glencoe/McGraw-Hill185 Glencoe GeometryLesson 4-1 Use a protractor to classify each triangle as acute,equiangular,obtuse,or the indicated type of xand the measure of each side of the !

6 ABCis equilateral with AB!3x#2,BC!2x"4, and CA!x" !DEFis isosceles,"Dis the vertex angle,DE!x"7,DF!3x#1, and EF!2x" the measures of the sides of !RSTand classify each triangle by its (0, 2),S(2, 5),T(4, 2) (1, 3),S(4, 7),T(5, 4)ECDAB Glencoe/McGraw-Hill186 Glencoe GeometryUse a protractor to classify each triangle as acute,equiangular,obtuse,or the indicated type of triangles if A!B!"A!D!"B!D!"D!C!,B!E!"E!D!,A!B! B!C!,and E!D! D!C!. Find xand the measure of each side of the !FGHis equilateral with FG!x"5,GH!3x#9, and FH!2x# !LMNis isosceles,"Lis the vertex angle,LM!3x#2,LN!2x"1, and MN!5x# the measures of the sides of !KPLand classify each triangle by its (#3, 2) P(2, 1),L(#2,#3) (5,#3),P(3, 4),L(#1, 1) (#2,#6),P(#4, 0),L(3,#1) entered the design at the right in a logo contest sponsored by a wildlife environmental group.

7 Use a many right angles are there?ACDEBP ractice Classifying TrianglesNAME _____ DATE _____ PERIOD _____4-14-1 Reading to Learn MathematicsClassifying TrianglesNAME _____ DATE _____ PERIOD _____4-14-1 Glencoe/McGraw-Hill187 Glencoe GeometryLesson 4-1 Pre-ActivityWhy are triangles important in construction?Read the introduction to Lesson 4-1 at the top of page 178 in your textbook. Why are triangles used for braces in construction rather than other shapes? Why do you think that isosceles triangles are used more often thanscalene triangles in construction?Reading the the correct numbers to complete each an obtuse triangle, there are acute angle(s),right angle(s), and obtuse angle(s).

8 An acute triangle, there are acute angle(s),right angle(s), and obtuse angle(s). a right triangle, there are acute angle(s),right angle(s), and obtuse angle(s). whether each statement is always,sometimes,or right triangle is obtuse triangle is equilateral triangle is a right equilateral triangle is acute triangle is scalene triangle is each triangle by as many of the following words as apply:acute,obtuse,right,scalene,isoscel es,or You good way to remember a new mathematical term is to relate it to a nonmathematicaldefinition of the same word. How is the use of the word acute,when used to describeacute pain,related to the use of the word acutewhen used to describe an acute angleoran acute triangle?

9 534135!80!70!30! Glencoe/McGraw-Hill188 Glencoe GeometryReading MathematicsWhen you read geometry , you may need to draw a diagram to make the texteasier to three points,A,B,and Con a coordinate y-coordinates of Aand Bare the same. The x-coordinate of Bisgreater than the x-coordinate of coordinates of Care greaterthan the corresponding coordinates of triangle ABCacute, right,or obtuse?To answer this question, first draw a sample triangle that fits the ABmust be a horizontal segment because the y-coordinates are the same. Point Cmust be located to the right and up from point the diagram you can see that triangle ABCmust be each question. Draw a simple triangle on the grid above to help three points,R,S,and three noncollinear points,Ton a coordinate grid.

10 The J,K,and Lon a coordinate grid. Thex-coordinates of Rand Sare they-coordinates of Jand Kare thesame. The y-coordinate of Tissame. The x-coordinates of Kand Lbetween the y-coordinates of Rare the same. Is triangle JKL acute,and x-coordinate of Tis lessright, or obtuse?than the x-coordinate of angleRof triangle RST acute, right, or obtuse? three noncollinear points, three points,G,H,and ID,E,and Fon a coordinate a coordinate grid. Points Gand The x-coordinates of Dand EareHare on the positive y-axis, andopposites. The y-coordinates of Dandthe y-coordinate of Gis twice the Eare the same. The x-coordinate ofy-coordinate of Iis on the Fis 0. What kind of triangle mustpositive x-axis, and the x-coordinate!