University:
Missouri State University
Course:
MTH 460 | College Geometry
Academic year:

2019
Views:

396

Pages:

3
Author:

Asa Carrillo

GEOMETRY/TRIGONOMETRY 2 Name KEY 3.3: Proving Lines Parallel Postulate 11 If two lines are cut by a transversal and corresponding angles are then the lines are parallel. Theorem 3-5 STATEMENTS DAI 543 ID GIVEN 2) CORE 255 E, LINES //. 2k//n If two lines are cut by a transversal and alternate interior angles are then the lines are parallel. t Given: 142 STATEMONYS RBASIN k 3 2 14522 2) k-//n GIVEN 2) 4-12.3 LINES // n 1 Prove: K-//n 1) 12. Statements Reasons 1) Given 2) 22 23 2) Venue. 55 3) 41343 4) k/ln 3) Substitution 4) CORR. 45, LINES // Theorem 3-6 If two lines are cut by a transversal and same-side interior angles are SUPPLEMENTARY then the lines are parallel. STATEMENTS 1724445180 REASONTS GIVEN a 144825 ARE 2) DAF of Supp. 15 Supp. Theorem 3-7 *) ssis SUPP, LINES // In a plane, two lines perpendicular to the same line are PARALLEL. C d Theorem 3-8 STATEMENTS i) cte; d Le 2) clld Through a point outside a line, there is exactly one line PARAVEL to the given line. REASONS DGIVEN 2 ) 2 LINES I to THE SAME LINE ARE. //. Theorem 3-8 Through a point outside a line, there is exactly one line PERPENDICULAR to the given line. (conn 2 / A * ri ) (55$) (a) State which segments must be parallel. FIND 45 (b) State the postulate or theorem that justifies your answer. 1) M 2 LINEF I to SAME LINE ARE 2) EU//FG OR Supp. 45 FiRST; FIND TRANSVERJAL, FIND LINES. Ai xs LINES // A X Y L M B 3) GB/FC CORR. 45 G LINES // F E A 53° 44° B 53° 45° D H E 48° 148 G 4) AD16C SSits Supp., LINES // A B 110° 112° C In each exercise, some information is given. Name the lines (if any) that must be parallel. If there are no such lines, write none. k illk 5) angle 1 cong angle8 NONE 6) angle 4 equiv angle6 illk 7) angle 10 approx angle7 illk 45 6 8) m angle3+m angle 4 = 180 8 9 9) angle 5 cong angle3 10 10) angle 6 cong angle7 P N NOPS P 11) angle 1 cong angle3 NONE 12) m angle1+m angle 4 = 180 1 2/3 13) angle 1 cong angle4 ORTS 14) angle 2 equiv angle5 0 R 4 NONE 15) angle 5 cong angle3 16) 4 is supp. to angle 5 5 To S Find the values of x that makes j || k. 17) x = 15 18) x = 10 ssi 45 Aix's t * 0 = x 3x + 10 = 5x * 0.1 200 = 2x 6x (5x + 15) deg 11x + 15 = 180 11x = 165 11-15 6x + 5x + 15 = 180 (3x+10) Tk (5x-10) k N*o_{N}*E overline No ||PS 70 deg Find the values of x and y that make AC || DF and AE || BF. 19) x = 20 y = 25/n A 20) x = 18 y = 26 B (3y-1) (5-7) (4-18) DE F A C (4x+5) D E F 5' * x - 13 = 4x + 5' 3y - 1 = 4x + 55 4x18-8x+2; 5y - 7 + 4x - 18 = 180 1 Complete the following proofs by supplying the missing statements and reasons. A C 21) Given: angle 3 is supplementary to angle 5 ; 2/3 B Prove: BD || FE Statements 4 D 5 F E Reasons 1) is supp. To underline < 5 1) GIVEN 2) 443 - M angle S=tB0 3) angle 3 = angle4 4) m angle4+m angle 5 = 180 5) angle 4 is supplementary to angle 5 6) 80/11 FE 2) DEF. OF SUPP 45 3) VERTICAL AS 4) SUBstitution 5) DEF OF Supp. 45 6) 55is Supp, LINES// 22) Given: jllk; Prove: || n 2 3 5 k 4 Statements. 1) jllk 1) GIVEN 2) 4522 Reasons 2) LINES 11, CORRAS 3) angle 1 cong/3 3) GIVEN 4) 4) Substitution 5) Illn 5) CORR AS LIVES// angle 1 cong angle3 (3r + 2) deg (5x - 13) ^ 6