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Geometry: Angles and Parallel Lines Practice Problems

Practice problems focusing on angles and parallel lines with corresponding angle postulates and theorems. Examples provided with step-by-step solutions.

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Geometry: Angles and Parallel Lines Practice Problems

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  1. Choose the segment skew to MP. Warm ups Choose the plane parallel to plane MNR. Classify the relationship between <1 and <5. Classify the relationship between <3 and <8. Classify the relationship between <4 and <6.

  2. 3-2 Angles and Parallel Lines

  3. If 2 parallel lines are cut by a transversal, then corresponding angles are congruent. (Corr. Ang. Post) What 4 pairs are congruent? <1 & <5, <2 & <6, <3 & <7 and <4 & <8 Corresponding Angles Postulate 1 2 3 4 5 6 7 8

  4. Example In the figure, m<11 = 51. Find m<15. Tell which postulates (or theorems) you used. <15 is congruent to <11: Corr. Ang. Postulate Answer: m<15 = 51

  5. Example In the figure, m<11 = 51. Find m<16. Tell which postulates (or theorems) you used. <16<15 Vertical Angles Theorem <15<11Corr. Ang. Post. <16<11 Transitive Property Answer: m<16 = 51

  6. Example In the figure, a || b and m<18 = 42. Find m<22. A. 42 B. 84 C. 48 D. 138

  7. Example In the figure, a || b and m<18 = 42. Find m<25. A. 42 B. 84 C. 48 D. 138

  8. If 2 parallels are cut by a transversal, then alternate interior angles are congruent. (Alt. Int. Thm) What 2 pairs of angles are congruent? <3 & <6, <4 & <5 Alternate Interior Angles Theorem 1 2 3 4 5 6 7 8

  9. If two parallels are cut by a transversal, then consec. interior angles are supplements. (CIA Thm) CIA are the only one that is SUPPS!! (Bracket) What 2 pairs are supps? <3 + <5 = 180, <4 + <6 = 180 Consecutive Interior Angles Thm 1 2 3 4 5 6 7 8

  10. If 2 parallels are cut by a transversal, then alternate exterior angles are congruent. (Alt. ext. Thm) What 2 pairs of angles are congruent? <1 & <8, <2 & <7 Alternate Ext. Angles Theorem 1 2 3 4 5 6 7 8

  11. Example FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m<2 = 125, find m<3. <2 <3 Alternate Interior Angles Theorem Answer:m<3 = 125

  12. Example FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m<2 = 125, find m<4. A. 25 B. 55 C. 70 D. 125

  13. Example ALGEBRAIf m<5= 2x – 10, and m<7 = x + 15, find x. <5 <7 Corresponding Angles Postulate 2x – 10=x+ 15 x – 10= 15 x = 25 Answer:x = 25

  14. Example (watch the WB if you get lost) If m<4= 4(y – 25), and m<8 = 4y, find y. <8<6Corr. Ang. Post. m<6 + m<4= 180 Supplement Theorem 4y + 4(y – 25) = 180 4y + 4y – 100 = 180 8y = 280 Add 100 to each side. y = 35 Divide each side by 8. Answer:y = 35

  15. TWAP!!!!! Think!!! A. ALGEBRA If m<1= 9x + 6, m<2= 2(5x – 3), and m<3= 5y + 14, find xand y. A.x = 9, y =14 B.x = 12, y = 20 C.x = 12, y = 14 D.x = 14, y = 12

  16. If a transversal is perp. to one of two parallel lines, then it is perp. to the other line as well. Perp. Transversal Thm.

  17. Homework • Pg. 183 # 11 – 19, 25, 27, 29, 36, 43, 46

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