Unit 3 Review Pcket nswer Key Section I Nme the five wys to prove tht prllel lines exist. 1. If two lines re cut y trnsversl nd corresponding ngles re congruent, then the lines re prllel.. If two lines re cut y trnsversl nd lternte interior/exterior ngles re congruent, then the lines re prllel. 3. If two lines re cut y trnsversl nd sme side interior/exterior ngles re supplementry, then the lines re prllel. 4. If two lines re prllel to third line, then the lines re prllel.. If two lines re perpendiculr to third line, then the lines re prllel. Section II Identify the pirs of ngles. If the ngles hve no reltionship, write none. 1. 7 & 11 None. 3 & lternte Interior ngles 3. 8 & 1 orresponding ngles 1 3 4 9 10 11 1 4. & 7 lternte Exterior ngles. 3 & Sme Side Interior ngles 7 8 13 14 1 1. 1 & None 7. 1 & None 8. 1 & 4 Verticl ngles Section III Fill In Verticl ngles re congruent. If two prllel lines re cut y trnsversl, then corresponding ngles re congruent. If two prllel lines re cut y trnsversl, then lternte interior ngles re congruent. If two prllel lines re cut y trnsversl, then lternte exterior ngles re congruent. If two prllel lines re cut y trnsversl, then sme side interior ngles re supplementry. If two prllel lines re cut y trnsversl, then sme side exterior ngles re supplementry.
Unit 3 Review Pcket Pge nswer Key Section IV etermine which lines, if ny, re prllel sed on the given informtion. 1.) m 1 = m 9 c // d.) m 1 = m 4 None 1 3 4 9 10 11 1 3.) m 1 + m 14 = 180 // 7 8 13 14 1 1 4.) m 1 = m 13 None c d.) m 7 = m 14 c // d.) m 13 = m 11 None 7.) m 1 + m 1 = 180 None 8.) m 4 = m // Section IV etermine which lines, if ny, re prllel sed on the given informtion. 1. m 1 = m 4 //. m = m 8 t // s 3. 1 nd 11 re supplementry None 4. ^ t nd ^ t //. m 14 = m None. nd 7 re supplementry t // s 1 k m 7. m 14 = m 1 k // m 13 1 11 10 9 8 7 t 8. 7 nd 8 re supplementry None 9. m = m 10 k // m 1 3 4 s 10. m 1 = m 13 None 14
Unit 3 Review Pcket Pge 3 nswer Key Section V - Proofs J 1. Given: GK isects JGI; m 3 = m Prove: GK // HI G 1 K 1. GK isects JGI 1. Given. m 1 = m. efinition of n ngles isector H 3 I 3. m 3 = m 3. Given 4. m 1 = m 3 4. Sustitution. GK // HI. If two lines re cut y trnsversl nd corresponding ngles re congruent, then the lines re prllel.. Given: J // K; m 1 = m Prove: // FE 1. J // K 1. Given. m 1 = m 3. If two prllel lines re cut y trnsversl, then corresponding ngles re congruent. 3. m 1 = m 3. Given F J 1 3 4 K E 4. m 3 = m 4. Sustitution. // FE. If two lines re cut y trnsversl nd corresponding ngles re congruent, then the lines re prllel.
Unit 3 Review Pcket Pge 4 nswer Key 3. Given: // ; 3 @ 4 Prove: 10 @ 1 1 3 4 1. // 1. Given. 4 @ 7. If two prllel lines re cut y trnsversl then lternte interior ngles re congruent. 10 c 7 8 9 d 3. 3 @ 4 3. Given 4. 3 @ 7 4. Sustitution. 1 @ 3; 7 @ 10. Verticl ngles Theorem. 10 @ 1. Sustitution 4. Given: 1 nd 7 re supplementry. Prove: m 8 = m 4 8 4 7 1 3 1. 1 nd 7 re supplementry 1. Given. m 1 + m 7 = 180. efinition of Supplementry ngles 3. m + m 7 = 180 3. ngle ddition Postulte 4. m 1 + m 7 = m + m 7 4. Sustitution. m 1 = m. Sutrction Property. //. If two lines re cut y trnsversl nd corresponding ngles re congruent, then the lines re prllel. 7. m 8 = m 4 7. If two prllel lines re cut y trnsversl, then corresponding ngles re congruent.
Unit 3 Review Pcket Pge nswer Key. Given: ST // QR; 1 @ 3 Prove: @ 3 P 1. ST // QR 1. Given S 1 3 T. 1 @. If two prllel lines re cut y trnsversl, then corresponding ngles re congruent. Q R 3. 1 @ 3 3. Given 4. @ 3 4. Sustitution. Given: E isects ; 1 @ 3 Prove: // E 1. E isects 1. Given. @ 3. efinition of n ngle isector 3. 1 @ 3 3. Given 4. @ 1 4. Sustitution. // E. If two lines re cut y trnsversl nd lternte interior ngles re congruent, then the lines re prllel. 3 1 E
Unit 3 Review Pcket pge nswer Key 7. 1. // 1. Given Given: // ; // E Prove: @. @ 4. If two prllel lines re cut y trnsversl, then lternte interior ngles re congruent. 3. // E 3. Given 4. 4 @ 4. If two prllel lines re cut y trnsversl, then lternte interior ngles re congruent.. @. Sustitution 1 3 4 7 E 8. 1. // 1. Given Given: // ; @ Prove: // E. @ 4. If two prllel lines re cut y trnsversl, then lternte interior ngles re congruent. 3. @. Given 4. 4 @ 4. Sustitution. // E 3. If two lines re cut y trnsversl nd lternte interior ngles re congruent, then the lines re prllel. 1 3 4 7 E
Unit 3 Review Pcket pge 7 nswer Key Section VI Solve ech lger onnection Prolem. 1.. w 4x - 3y z + 7 x 1 37 y w = 37 x = 143 y = 71. z = 8 x = 3/ y = 3. 4. 30 x + 1 7 y x x 8x + 1 x = 1 y = 7 x = 11. 4x + 13 4x +. x 4x + 17 x x 80 83 4x + 4x + 13 x = 3 x = 0 Is //? yes Is //? no
Unit 3 Review Pcket pge 8 nswer Key Numer of Sides Nme of polygon Sum of interior ngles. Mesure of ech interior ngle if it ws regulr polygon Sum of the Exterior ngles Mesure of ech exterior ngle if it ws regulr polygon. Numer of igonls tht cn e drwn. 3 Tringle 180 0 30 10 0 4 Qudrilterl 30 90 30 90 Pentgon 40 108 30 7 Hexgon 70 10 30 0 9 7 Heptgon OR Septgon 900 18.7 30 1.43 14 8 Octgon 1080 13 30 4 0 9 Nongon 10 140 30 40 7 10 ecgon 1440 144 30 3 3 n n-gon 30 ( n )180 ( n )180 n 30 n n(n 3)