01 Ge08cs FM I - Manor Alternative Placement

and Chapter 2, p. 72.214Chapter 43.0, and16.0 are also covered in this chapter. To see these standards unpacked, go to Chapter 1,

Reading Strategy: Read Geometry SymbolsIn Geometry we often use symbols to communicate information.When studying each lesson, read both the symbols and the words slowly andcarefully. Reading aloud can sometimes help you translate symbols into words.!"!RAY ÊWENDPOINT ITHAT POINT Ȝ89:MȜ89:ANGLE 89 WITHVERTEX AT 9MEASURE OFANGLE 89 ûRIGHT ANGLEPI!"LINE ɁNOT *CONGRUENTPERPENDICULARPLANE SEGMENT ȸ0ʡ !"]X]ABSOLUTEVALUE OF ÝȡIF THENPARALLELThroughout this course, you will use these symbols and combinations of thesesymbols to represent various geometric statements.Symbol Combinations ST BC UV GHp qTranslated into WordsLine ST is parallel to line UV.Segment BC is perpendicular to segment GH.If p, then q.m QRS 45 The measure of angle QRS is 45 degrees. CDEAngle CDE is congruent to angle LMN. LMNTry ThisRewrite each statement using symbols.1. the absolute value of 2 times pi2. The measure of angle 2 is 125 degrees.3. Segment XY is perpendicular to line BC.4. If not p, then not q.Translate the symbols into words.5. m FGH m VWX6. ZA TU 7. p q bisects TSU.8. STTriangle Congruence215

4-1ClassifyingTrianglesWho uses this?Manufacturers use properties oftriangles to calculate the amount ofmaterial needed to make triangularobjects. (See Example 4.)ObjectivesClassify triangles bytheir angle measures andside lengths.Use triangle classificationto find angle measuresand side lengths.Vocabularyacute triangleequiangular triangleright triangleobtuse triangleequilateral triangleisosceles trianglescalene triangleA triangle is a steel percussion instrumentin the shape of an equilateral triangle.Different-sized triangles producedifferent musical notes when struckwith a metal rod.Recall that a triangle ( ) is a polygonwith three sides. Triangles can beclassified in two ways: by their anglemeasures or by their side lengths. AB, BC, and AC are the sides of ABC.A, B, and C are the triangle’s vertices. Triangle ClassificationEXAMPLE1By Angle MeasuresAcute TriangleEquiangular TriangleRight TriangleObtuse TriangleThree acuteanglesThree congruentacute anglesOne rightangleOne obtuseangleClassifying Triangles by Angle Measures Classify each triangle by its angle measures.California Standards12.0 Students find and usemeasures of sides and of interiorand exterior angles of triangles andpolygons to classify figures andsolve problems.ÎäÂA EHG EHG is a right angle. Soa right triangle.EHG isÈäÂÈä B EFH EFH and HFG form a linear pair, so they are supplementary.Therefore m EFH m HFG 180 . By substitution,m EFH 60 180 . So m EFH 120 . EFH is anobtuse triangle by definition.1. Use the diagram to classify216ÎäÂChapter 4 Triangle CongruenceFHG by its angle measures.

Triangle ClassificationEXAMPLE2By Side LengthsEquilateral TriangleIsosceles TriangleScalene TriangleThree congruent sidesAt least twocongruent sidesNo congruent sidesClassifying Triangles by Side LengthsClassify each triangle by its side lengths. A ABC From the figure, AB AC. So AC 15,and ABC is equilateral.When you look at afigure, you cannotassume segments arecongruent based ontheir appearance.They must be markedas congruent. n xB ABDxBy the Segment Addition Postulate,BD BC CD 15 5 20.Since no sides are congruent, ABD is scalene.2. Use the diagram to classifyEXAMPLE x3ACD by its side lengths.Using Triangle ClassificationFind the side lengths of the triangle.Step 1 Find the value of x. JK KLJK KL(4x - 1.3) (x 3.2)3x 4.5x 1.5xÝÊ Êä Ó Given{ÝÊ Ê ÎÝÊ Ê

angle One obtuse angle Triangle Classification By Angle Measures EXAMPLE 1 Classifying Triangles by Angle Measures Classify each triangle by its angle measures. A EHG Îä Îä ÈäÂÈä EHG is a right angle. So EHG is a right triangle. B EFH EFH and HFG form a linear pai