University:
Felician University
Course:
MATH-231 | Geometry I
Academic year:

2024
Views:

237

Pages:

2
Author:

Clint W.

Geometry Honors Name: KEY Period: Use the diagram for Exercises 35-40. 35. Name a pair of alternate interior angles with transversal n. ∠5 and ∠8 36. Name a pair of same-side interior angles with transversal f. ∠7 and ∠2 37. Name a pair of corresponding angles with transversal m. ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8 38. Identify the transversal and classify the angle pair for ∠3 and ∠7. l; corresponding angles 39. Identify the transversal and classify the angle pair for ∠5 and ∠8. n; alternate interior angles 40. Identify the transversal and classify the angle pair for ∠1 and ∠6. m; alternate exterior angles m∠RST = (x + 50)° and m∠STU = (3x + 20)°. Find m∠RST. x + 50 = 3x + 20 50 = 2x + 20 30 = 2x x = 15 m∠RST = 15 + 50 = 65° 6. Ocean waves move in parallel lines toward the shore. The figure shows Sandy Beaches windsurfing across several waves. For this exercise, think of Sandy's wake as a line. m∠1 = (2x + 2y)° and m∠2 = (2x + y)°. Find x and y. 2x + 2y = 110 2x + y = 70 y = -2x + 70 2x + 2(-2x + 70) = 110 2x - 4x + 140 = 110 -2x = -30 x = 15 y = -2(15) + 70 y = 40 Use the figure for Exercises 1-8. Tell whether lines m and n must be parallel from the given information. If they are, state your reasoning. (Hint: The angle measures may change for each exercise, and the figure is for reference only.) 1. m∠7 = 23°, m∠6 = 23° YES, converse of same-side interior angles theorem 2. m∠1 = (15x + 22)°, m∠3 = (8x - 5)° x = 14 m∠1 = 15(14) + 22 = 232° m∠3 = 8(14) - 5 = 107° NO, same-side interior angles should be supplementary 3. ∠7 ≅ ∠6 YES, converse of corresponding angles postulate 4. m∠2 = (5x + 3)°, m∠3 = (8x - 5)° x = 14 m∠2 = 5(14) + 3 = 73° m∠3 = 8(14) - 5 = 107° NO - converse of same-side interior angles postulate 5. m∠8 = (6x - 1)°, m∠4 = (5x + 3)°, x = 9 m∠8 = 6(9) - 1 = 53° m∠4 = 5(9) + 3 = 48° NO - converse of alternate exterior angles postulate 6. ∠5 ≅ ∠7 YES - converse of corresponding angles postulate 7. ∠1 ≅ ∠5 NO - corresponding angles can never be congruent 8. m∠6 = (x + 10)°, m∠2 = (x + 15)° x + 10 = x + 15 0 = 5 NO - angles can never be congruent P. 181, #1-16 1. AE ⊥ AB 2. AB || FG, arc skew 3. AE || FB 4. PEF || DHG 5. ∠3 ≅ ∠5 6. ∠4 ≅ ∠6 7. ∠2 ≅ ∠7 8. ∠1 ≅ ∠6 9. 135° - corr. ∠s 10. 15x - 7 = 19x - 15 -7 = 4x - 15 8 = 4x x = 2 ∠1 = 23° 11. 43x + 36 = 54x + 14 - alt. ext. ∠s 36 = 11x + 14 22 = 11x x = 2 ∠1 = 122° 12. m∠8 = 3(3) + 20 = 29 + 20 = 59° m∠6 = 7(3) + 38 = 21 + 38 = 59° m∠8 = m∠6 ∠8 ≅ ∠6 a || b - conv. of the corr. ∠s Post. 13. ∠1 ≅ ∠5 a || b - conv. of the alt. ext. ∠s Thm 14. m∠8 + m∠7 = 180 a || b - conv. of the same-side int. ∠s Thm 15. m∠3 = m∠4 ∠3 ≅ ∠4 a || b - conv. of the alt. int. ∠s Thm The guy wires are || by the conv. of the corr. ∠s Post. 16. m∠1 = 3(14) + 12 m∠1 = 54° m∠2 = 4(14) - 2 m∠2 = 54° m∠1 = m∠2 ∠1 ≅ ∠2 The guy wires are || by the conv. of the corr. ∠s Post.