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Welcome to Geometry B! w3 m ke i+ c unt This Week at a Glance Return Ch. 6 Quizzes 6.5 Notes Assignment: 6.5 Worksheet Monday: 6.5 Altitudes & Angle Bisectors Tuesday: Ch. 6B Review Wednesday: Ch. 6B Test Thursday: 7.0 Radical Review Friday: 7.1 Geometric Means Monday: 6.5 Altitudes & Angle Bisectors Tuesday: Ch. 6B Review Wednesday: Ch. 6B Test Thursday: 7.0 Radical Review Friday: 7.1 Geometric Means • I can use proportions to find relationships using altitudes and angle bisectors in triangles Think about a triangle drawn on a piece of paper being placed in a copy machine and either enlarged or reduced. The copy is similar to the original triangle. Suppose you drew in special segments of a triangle, such as the altitudes or angle bisectors on the original. When you enlarge or reduce that original triangle, all of those segments are enlarged or reduced at the same rate. Word Definition A perpendicular segment from a ALTITUDE vertex to the line containing the opposite side. ANGLE BISECTOR A segment whose endpoints are one vertex of a triangle and the opposite side. Example THEOREM: If two triangles are similar, then the measures of the corresponding proportional to altitudes are _________________ the measures of the corresponding If SH and FJ are altitudes and RST ~ EFG, then SH RS FJ EF sides. If AD and MQ are altitudes and ACB ~ MPN, then AD AB MQ MN Find FG if RST ~ EFG, SH is an altitude of RST, FJ is an altitude of EFG. ST = 6, SH = 5, and FJ = 7. 5 6 7 x 5 7 = 6 x 5x = 42 x = 8.4 ABC ~ MNP, AD and MQ are altitudes, AB = 24, AD = 14, and MQ = 10.5. Find MN. 14 24 14 10.5 x 10.5 = 24 x 14x = 252 x = 18 ZXY ~ TRS. Find XY, XZ, and ZY. 10 XY 5 8.7 10 XZ 5 6 10 ZY 5 13 5xy = 87 5xz = 60 5xz = 130 xz = 12 zy = 26 xy = 17.4 Find ZB if STU ~ XYZ, UA is an altitude of STU, ZB is an altitude of XYZ, UT = 8, UA = 6, and ZY = 12. THEOREM: An angle bisector in a triangle separates the opposite side into G segments that have the same ratio as the other two sides. If GC is an angle bisector, then AG AC AC CB or GB BC AG GB Find the value of x. 20 7 = 24 x 20x = 168 x = 8.4 Find the value of x. x = x+7 11 17 17x = 11(x + 7) 17x = 11x + 77 6x = 77 x = 12.83 Find RV and VT. 14 10 = x+2 2x + 1 RV = 3 + 2 = 5 VT = 2(3) + 1 = 7 10(2x + 1) = 14(x + 2) 20x + 10 = 14x + 28 6x + 10 = 28 6x = 18 x=3 Find the value of x. ASSIGNMENT 6.5 Worksheet Skip #3, 6, 9