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HW #4—Geometry Review for Test #3 KEY Name:_____________________________ Period:_____ Define & give an example and/or a picture of each of the following; make a notecard/flashcard for each. **USE YOUR BOOK FOR DEFINITIONS** 1. Complementary Angles 12. Def. of Midpoint 2. Supplementary Angles 13. Segment Addition Postulate 3. Vertical Angles 14. Distributive Property 4. Adjacent Angles 15. Parallel Lines 5. Linear Pair Theorem 16. Skew Lines 6. Angle Addition Postulate 17. Transversal 7. Obtuse angle 18. CBT – Cut by Transversal 8. Right angle 19. Perpendicular Lines 9. Acute angle 20. Corresponding Angles 10. Straight angle 21. Alternate Interior Angles 11. Def. of Angle Bisector 22. Same-side Interior Angles Solve: 23. 5x + 3(2x – 4) = 2(4 + 3x) – 6 24. X = 14/5 or 2.8 4(x + 6 ) = 2(2x – 10) NO SOLUTION Solve each system of equations; write your answer as an ordered pair. 25. 3 x – 2 y = 12 3 x – y = 18 26. 5 x + 2 y = 13 3 x – 4 y = 26 (8, 6) (4, -3.5) For 27-30 write the key theorem, write an equation and solve for x, and find all indicated angles. 27. Solve for x and find m<1, m< 3, and m<4 m<1 = 12x + 4 m<2 = 148 VERTICAL ANGLES THM. X = 12 2 32o 3 4 1 148o 32o SHOW ALL WORK OR NO CREDIT! 28. Solve for x and find m<1 and m<2; m<1 = 4(2x + 6) m<2 = 3x + 39 and a // b CORRESPONDING ANGLES POST. X=3 48o 1 a 48o 2 b SHOW ALL WORK OR NO CREDIT! 29. Solve for x and find m<1 and m<2; a // b m<1 = 5(3x + 2) m<2 = 10(2x – 4) a ALTERNATE INTERIOR ANGLES THM. X = 10 b 1 160o SHOW ALL WORK OR NO CREDIT! 160o 2 30. Solve for x and find m<1 and m<2; a // b m<1 = 4(x + 3) + 6 m<2 = 6(x + 2) SHOW ALL WORK OR NO CREDIT! SAME SIDE INTERIOR ANGLES THM. X = 15 a 102o 2 78o 1 b You MUST also do these pages from your textbook—Show all work or no credit, and check the answers in the back of the book! Book pages: 202-204 problems (1-3 and 6-23) 1. Alternate interior angles 2. Skew Lines 3. Transversal 4. 5. 6. DE and BC are skew (possible answer) 7. AB || DE 8. 𝑨𝑫 ⊥ 𝑫𝑬 9. Plane ABC || plan DEF 10. Transversal: l; alt. int. angles 11. Transversal: n; corresponding angles 12. Transversal: l; same-side interior angles 13. Transversal: m; alt. ext. angles 14. 90o 15. 100o 16. 79o 17. 76o 18. c || d by the Conv. of alt. int. angles thm. 19. m<1 = 107o and m<5 = 107o, so ∠𝟏 ≅ ∠𝟓, c || d by the conv. of corr. Angles post. 20. m<6 = 66o, m<3 = 114o, 66 + 114 =180, so <6 and <4 are supplementary. c || d by the conv. of same side int. angles thm. 21. m<1 = 99o and m<7 = 99o, so ∠𝟏 ≅ ∠𝟕… c || d by the conv. of the alt. ext. angles thm. 22. KM 23. x – 5 < 8; x < 13