C. Parallel Lines (AB||CD) NOTE: < = Angle ^ = Degrees Make sure you know these theorems, definitions and assumptions. :RA :SB :SH11311 3 :SH09332 :SH13334 :SP196052259116259116259116 :SP259052196116196116196116 :SF 1. If two straight lines intersect, the pairs of opposite angles formed are called vertical angles and are equal. The pairs of adjacent angles are supplementary and equal 180^. Vertical Angles: angle <1 = <3 <2 = <4 Supplementary Angles: <1 + <2 = 180^ <2 + <3 = 180^ <3 + <4 = 180^ <4 + <1 = 180^ :RA :SD :SB :SH0927l :SH1327m :SH08361 2 :SH10334 3 :SH12315 6 :SH14298 7 :SP193068266068266068266068 :SP193100266100266100266100 :SP265050196120196120196120 :SF 2. If two straight lines are parallel (never meeting) and are cut by a transversal (a line that touches each of the parallel lines): a. the pairs of alternate interior angles are equal; b. the pairs of corresponding angles are equal; c. the pairs of interior angles on the same side of the transversal are supplementary. :RA If line l is parallel to line m: a. Alternate interior angles <3 = <5 <4 = <6 b. Corresponding angles <1 = <5 <4 = <8 <2 = <6 <3 = <7 c. Interior angles on the same side of the transversal <4 + <5 = 180^ <3 + <6 = 180^ :RA Notice that there are many pairs of vertical angles and supplementary angles. Vertical Angles <1 = <3 <2 = <4 <5 = <7 <6 = <8 Supplementary Angles <1+<2 = 180^ <5+<6 = 180^ <2+<3 = 180^ <6+<7 = 180^ <3+<4 = 180^ <7+<8 = 180^ <4+<1 = 180^ <8+<5 = 180^ :RA :SD :Q :SB :SP198028264028264028264028 :SP198070264070264070264070 :SP244012217082217082217082 :SH0428A :SH0439B :SH0928C :SH0939D :SH0236E :SH1133F :SH0533a :SH0834b :SH0336c :SH0535d :SH1031e :SF 1. If <d = 150^ and AB||CD, find the number of degrees in <e. (a) 30 (b) 60 (c) 150 (d) 180 (e) It cannot be determined from the information given. :RCA 1. (a) 30 Ans. Because <a and <d are supplementary <a = 180^ - <d <a = 30^ <a and <e are corresponding angles and therefore equal <e = <a = 30^ Ans. :RA :Q 2. Given: <a = 3y + 5^, <b = 2y + 11^. Find the number of degrees in <a. (a) 6 (b) 16 (c) 23 (d) 43 (e) 0 :RCC 2. (c) 23 Ans. Since <a and <b are alternate interior angles, <a = <b 3y + 5 = 2y + 11 y = 6^ a = 3 (6^) + 5^ = 23^ Ans. :RA :Q 3. Angle b = 4m^ and angle d = 5m^. Find the value of m. (a) 10 (b) 20 (c) 40 (d) 50 (e) 80 :RCB 3. (b) 20 Ans. Angle b and <d are interior angles on the same side of the transversal and therefore total 180^ 4m^ + 5m^ = 180^ m = 20^ Ans. :RA :SD :Q :SB :SH0528A B :SH0828C D :SH0434y :SH0932140^ :SP198036275036275036275036 :SP198060275060275060275060 :SP252024203072203072203072 :SF 4. AB || CD. Find the number of degrees in angle y. (a) 40 (b) 50 (c) 90 (d) 140 (e) 180 :RCD 4. (d) 140 Ans. y is a corresponding angle to the vertical angle equal to 140^ and is therefore also equal to 140^ Ans. :RA :SD :Q :SB :SH0427A x B :SH0627C D :SH0827E G :SH0234F H :SH0734y :SP189032266032266032266032 :SP189047266047266047266047 :SP231016189056189056189056 :SP266016224056224056224056 :SF 5. AB || CD, and EF || GH and <x = 30. Find the number of degrees in angle y. (a) 30 (b) 60 (c) 90 (d) 150 (e) 180 :RCD 5. (d) 150 Ans. y is a corresponding angle to the supplementary angle equal to 30^ therefore: y + 30^ = 180^ y = 150^ Ans. :SD :ET :ET
