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1 NAME Practice A For use with pages Find the measure of the indicated arc or angle. 1. mbc=? 2. mbc= B 3. m!-bac =? 160 C 4. mbc =? A 5. m/_bac = 6. m/_bac =? Find the measure of the arc or angle in maqmp 8. manmo 9. m~pno lo.m~@np 11. m@o 12. mnop 13. mp@ 14. mo@n Decide whether a circle can be circumscribed about the quadrilateral Find the value of each variabhe Chapter I 0 Resource Book Copyright McD0ugal Littell Inc. All rights reserved.
2 NAME. Practice B For use with pages Find the measure of the indicated arc or angle in 1. m/_bac=? 2. mbc =? 3. ma.bac=? B A Find the measure of the arc or angle in 0, given mcd = 108 and robe = ~lo0. 4. m/_abc 5. maced 6. ma.bde 7. macbd 8. maabd 9. m/-.bce 10. mad 11. nv~bc A E D Find the value of x. 2x+ 13) 16. (3x- 8) , Archeology Archeologists found a portion of a circulm" dinner plate. Describe a method to determine the diameter of the plate, Copyright McD0ugal Littett Inc. All rights reserved, (~eometry Chapter 10 Resource Book
3 NAME Pr~~*i~e A Far use with pages Find the measure of L ~ ~ 8, 92o~ Write an equation that can be used to so~ve for x. Then solve the equation for x. 105 Use the diagram of A to write the m/_l, m!_2, and m/_3 in order of increasing measure Geometry Copyright McD0ugal Litt~tl inc. I Cha~ter 10 Resource Book A ~ ght~ i~d. ~1
4 NAME Practic~ B For use with pages Find the measure of/_ , 1~) 241 ~ Write an equation that can be used to serve for x. Then solve the equation for x. 13. Aerial V~ew You are flying across the plains of Kansas at an altitude of 32,000 feet,~.or approximately 6 miles. It is a clear day. Find the measure of CD that represents the part of Earth that you can see. B not drawn to scale Copyright McDougal Littell Ins, All rights reserved. Geometry Chapter 10 Resource Book
5 Lesson 10.2 continued 5. Sample answer: Construct perpendicular bisectors of D --~ and ~. We may label the bisectors ~ and ~, where C is the center of the circle, K is the midpoint of DG and L is the midpoint of ~-~. Then CK ~ CL, because congruent chords are equidistant from the center, mad CJ ~ C J, by the Reflexive Property of Congruence. Therefore, by the HL Congruence Theorem, AKJC.~ ALJC; this gives!.d J1 ~ / HJI becaus.~e correspond~ag parts of ~Asare~-. 6. rode = 50,reEF= 130, mfg=50,mgd= Lesson 10.3 Warm-~Jp Exercises (40, 20) Daily Homework (~uiz 1. major arc 2, minor arc Lesson Opener Allow 15 minutes. 1. Sample answer: 2. m/_adb = m/_bca; The rays that form each angle intersect the circle at A and B, the endpoints of arc AB. 3. m!-dac = m/-cbd; arc CD 4, MP = MQ Practice A no 16. yes 17. yes 18. x= 180, y= x=55, y= x = 75 Pract[ce B Sample answer: Draw a chord, construct ± bisector; draw a second chord and construct ± bisector. Where ± bisectors intersect is the center. Measure radius. Double for diameter. Practice C , , ! , 20 16, Statements 1. /_MEI~ /.GED 2. m/.imd = ~ mid 3. m!.igd = ~ mid 4. m/_imd = m/.igd 6. AMEI~ AGED 1, Vert. Angles Tl~m. 2. Measure of inscribed/- = ½ measure of intercepted arc. 3. Measure of inscribed/- = ½ measure of intercepted arc. 4. Trans. Prop. of AA Similarity Postulate Regeach~ng with Practice I, , x=40, y=93 8. x=56, y=20 9. x=30, y~59.3 Reel-Li~e Application 1. /-BDC miles 3, about 3666 miles Challenge: Skills and Applications 1. Sample answer: Draw D--~. Since D--ff is a dianaeter,!.dgf is a right angle inscribed in C; therefore, DG ± FG. So, we have FG -~ GE (given),!.dgf ~!.DGE (all right angles are Copyright McD0ugal Littell Inc. All rights reserved, Geome ~ry Chapter 10 Resource Book
6 Lesson 10.3 continued congruent), and DG ~ DG (Reflexive Property of Congruence). By the SAS Congruence Postulate, ADGF ~ ADGE, so DF -~ DE (corresponding parts of = As are ~.) and ADEF is isosceles. 2. Sample answer: Draw PR, PS, and PT. Since PR is a diameter of Q,/-PSR is a right angle inscribed in Q; therefore, PS ± RT. APSR and APST are right triangles, PR ~ PT (radii of a circle are congruent), and PS =-- PS (Reflexive Property of Congruence). Therefore, APSR ~ APST by HL Congruence Theorem, and so RS -=- ST (corresponding parts of ~- As are ~). 3. Sample answer: Draw ~. Note that W Z II ~, so by the Alternate Interio.o_.rr Angles Theorem, /_WZX ~!_YXZ. But mwx = 2m/_WZX and myz = 2m/_YXZ, so mwx ~ YZ. Since two minor arcs in the same circle are congruent if and only if their corresponding chords are congruent, we conclude that WX ~- YZ, so WXYZ is an isosceles trapezoid. 4, a. OR = c, PS = c-a b. right triangle PS PQ co Sample answer: -- = -- PQ RP c-a b d. Sample answer: b c + a b 2 = (c-a)(c+a)=c ~- a 2,soa~ + b ~=ca. Quiz I ent~ li~ss~t ~the~xadi~u&dr &wn~tn o~~ the point of tangency ; two tangent segments with the same exterior endpoint are congruent Warm-Up l=xercises DaRy Homework Quiz 1. a=90,b=58,c=45 2. x=6, y=9 Lesson Opener Allow 10 minutes. 1. a. A b. D,E,F c. B,C 2. a. A,B,F, b. E e. C,D & ~. C,E b. B,D c. A,F Practice A & = ½(180 - x ); = ½(105 + x ); = ½(360 - x ); 168 l& m/_3, m/_2, m/-1 ~4. m~l,m~2, m~3 Practice ~ =½(360 -x ); = ½(125 - x ); = ½(x + 69 ); = ½(360 - x - x ); 135 1~. 17 = ~(x - 42 ); =~(360-x) ;84 ~3. ~6.3 Practice C Statements 1. C is midpt, of BD 2. BC ~ CD m~bac = mbc m/-cad = ~ mcd 4. mbc = mcd ~. ma_bac = mz_cad 7. AC bisects Z_BAD Reasons 1. Given 2. Def. of midpoint 3. In a, measure of inscribed/- = ½ 4. Congruent arcs have = measure 5. Mult. Prop. of Equality & Substitution 7. Def of Z_ bisector Geometry C0pyright McDougal Littel[ Inc;... Ch&pter 10 Resource Book All rights reserved.
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