CongruentTrianglesPreviously, you learned the following skills, which you’ll use in this chapter:classifying angles, solving linear equations, finding midpoints, and usingangle relationships.Prerequisite SkillsVOCABULARY CHECKClassify the angle asacute,obtuse,right, orstraight.1.m∠A511582.m∠B59083.m∠C53584.m∠D5958SKILLS AND ALGEBRA CHECKSolve the equation.5.7012y51806.2x55x2547.401x1655180Find the coordinates of the midpoint of}PQ.8.P(2,25),Q(21,22)9.P(24, 7),Q(1,25)10.P(h,k),Q(h, 0)Determine whether the angles are congruent.If so, explain why.11.∠2,∠312.∠1,∠413.∠2,∠614.∠3,∠4213546Before© Bill Ross/Corbis© Bill Ross/Corbis4.1Apply Triangle Sum Properties4.2Apply Congruence and Triangles4.3Relate Transformations and Congruence4.4Prove Triangles Congruent by SSS4.5Prove Triangles Congruent by SAS and HL4.6Prove Triangles Congruent by ASA and AAS4.7Use Congruent Triangles4.8Use Isosceles and Equilateral Triangles4.9Perform Congruence Transformations2044Lesson4.1CC.9-12.G.CO.104.2CC.9-12.G.CO.74.3CC.9-12.G.CO.64.4CC.9-12.G.CO.84.5CC.9-12.G.CO.84.6CC.9-12.G.CO.84.7CC.9-12.G.CO.104.8CC.9-12.G.CO.104.9CC.9-12.G.CO.2

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StartStartStatementReasons1.2.3.4.5.6.7.Given:Reasons:GivenGivenReflexive Property of Segment CongruenceAAS Congruence TheoremCorresponding parts of congruent triangles are congruent.Definition of Linear PairCongruent Supplements TheoremStatements:/RQTis supplementary to/1,and/RSTis supplementary to/2./1>/2/RTQ>/RTS/RQT>/RSTRT>RT$QRT>$SRTQT>STRT12QSStatementReasons1.2.3.4.5.6.7.Given:Reasons:GivenGivenReflexive Property of Segment CongruenceAAS Congruence TheoremCorredsponding ptartsfof congruet tt tnt trililiangles are congruent.Definition of Linear PairCongruent Supplements TheoremStatements:/RQTis supplementary to/1,and/RSTis supplementary to/2./1>/2/RTQ>/RTS/RQT>/RSTRT>RT$QRT>$SRTQT>STRT12QSIn this chapter, you will apply the big ideas listed below and reviewed in theChapter Summary. You will also use the key vocabulary listed below.Big Ideas1Classifying triangles by sides and angles2Proving that triangles are congruent3Using coordinate geometry to investigate triangle relationships• trianglescalene, isosceles,equilateral, acute, right,obtuse, equiangular• interior angles• exterior angles• corollary• congruent figures• corresponding parts• rigid motion• right trianglelegs, hypotenuse• flow proof• isosceles trianglelegs, vertex angle, base,base angles• transformationtranslation,reflection, rotationKEYVOCABULARYTriangles are used to add strength to structures in real-world situations. Forexample, the frame of a hang glider involves several triangles.GeometryThe animation illustrated below helps you answer a question from thischapter: What must be true about}QTand}STfor the hang glider to fly straight?Geometryat my.hrw.comWhy?NowScroll down to see the information neededto prove that}QT>}ST.

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