Math Geom Ch 3 Midterm Review Solutions

Chapter 3 Midterm Review Geometry CP Determine whether the given figure shows parallel, perpendicular, or skew lines. 1. a) The top of the fence & the basketball pole: skew b) The top of the fence & the fence posts: perpendicular c) The fence posts & the basketball pole:1 perpendicular   1. 2. a) XY and WZ: parallel b) XY and ZT: skew c) XY and YS: perpendicular d) XY and QT: parallel 3. Classify the following pairs of angles. a) ∠1 & ∠5: Corresponding angles b) ∠1 & ∠9: Corresponding angles c) ∠1 & ∠3: Vertical angles d) ∠1 & ∠4: Linear pair e) ∠2 & ∠8: Alternate Interior angles f) ∠3 & ∠8: Same Side Interior angles g) ∠3 & ∠9: Alternate Interior angles h) ∠9 & ∠15: Alternate Exterior angles i) ∠4 & ∠9: Same Side Interior angles Find the measure of ∠1 and ∠2. 4. m∠1 = 120° m∠2 = 60° 5. m∠1 = 140° m∠2 = 40° 6. m∠1 = 135° m∠2 = 45° 7. m∠1 = 110° m∠2 = 70° Find the value of x in each of the following diagrams. 8. 80 = 2x x = 40° 9. 120 = 3x x = 40° 10. 110 + 2x = 180 2x = 70 x = 35 11. 4x = 3x + 7 x = 7 12. 2x + 9 + 90 = 180 2x = 81 x = 40.5 Find the values of x and y in each of the following diagrams. 13. 3y + 31 + 6x + 8 = 180 3y + 58 = 118 y = 20 3(20) + 31 + 6x + 8 = 180 x = 6 14. x + 25 + 122 = 180 x = 33 3y + 58 + 118 = 180 3y = 8 y = 8/3 Section 1: Solving Equations for x and y 15. 5x + y = 130 10x = 80 Solving for x: x = 8 Substituting x = 8 into the first equation: 5(8) + y = 130, y = 76 16. x + 43 + 3y = 180 2y - 5 + 3y = 180 Solving for y: y = 34 Substituting y = 34 into the first equation: x + 43 + 3(34) = 180, x = 104 Section 2: Parallel Lines 17. Determine which lines are parallel (if any) based on the given angle relationships. a) ∠1 and ∠5: parallel b) ∠4 and ∠9: parallel c) ∠6 and ∠11: parallel d) ∠12 and ∠14: parallel e) ∠10 and ∠15: parallel 18. Complete the following proof: Given: ∠1 ≅ ∠2 and ∠3 ≅ ∠4 Prove: AB || CD Statements Reasons ∠1 ≅ ∠2 and ∠3 ≅ ∠4 Given ∠2 ≅ ∠3 Vertical Angles Theorem ∠1 ≅ ∠4 Substitution AB || CD Alternate Interior Angles Converse Section 3: Finding Slope 19. Find the slope of the line that passes through the given points. (2, 4) and (8, 4): m = 0 (5, 0) and (5, -4): m is undefined 20. Using slopes, determine if the lines are parallel, perpendicular, or neither. Line 1: (1, 1) and (3, 3) Line 2: (2, 2) and (0, 4) m₁ = 1, m₂ = -1, perpendicular Line 1: (-2, 3) and (-5, 2) Line 2: (4, 1) and (5, 3) m₁ = 1/3, m₂ = 2, neither Line 1: (-3, -2) and (1, 2) Line 2: (1, 3) and (4, 6) m₁ = 1, m₂ = 1, parallel Section 4: Graphing Lines 21. Graph the line with the given slope that passes through the given point. Line A: (1, 2), slope: 3 Line B: (-2, 1), slope: -1/2 Line C: (0, 2), slope: 1/2 Section 5: Writing Equations of Lines 27. Determine an equation for each line. Passes through (0, 4) with a slope of 2: y = 2x + 4 Passes through (2, 6) and (4, 12): y = 3x + 6 Passes through (2, 6) with a slope of -1/2: y = -1/2x + 7