Geometry Proofs: Parallel Lines and Angle Relationships, Exams of Nursing

A series of true/false and matching questions focused on geometric proofs related to parallel lines and angle relationships. It covers topics such as corresponding angles, supplementary angles, and alternate interior angles. The questions require students to match statements with reasons in proofs, identify correct conclusions based on given information, and complete two-column proofs. This material is suitable for high school geometry students learning about parallel lines, transversals, and angle theorems, offering practice in applying geometric principles and logical reasoning to solve problems.

Typology: Exams

2024/2025

Available from 08/31/2025

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Unit Three More Proofs for Postulates
9 and 10 Questions with Correct
Answers
True/False - Use the following figure to answer the question.
When line t is perpendicular to both line l and line m, then lines l and m are parallel. -
ANSWERSTrue
True/False - Use the following figure to answer the question.
If line t is perpendicular to both line l and line m, then angle 1 and angle 2 are both right
angles. - ANSWERSTrue
True/False - Use the following figure to answer the question.
If lines l and m are parallel, then angle 2 and angle 3 are corresponding angles. -
ANSWERSTrue
True/False - Use the following figure to answer the question.
If angle 1 and angle 2 are equal, then lines l and m are parallel. - ANSWERSTrue
Match the reasons with the statements in the proof to prove that lines l and m are
parallel, given that m2 = 122° and m3 = 58°
Given:
measure of angle 2 = 122°
measure of angle 3 = 58°
Prove:
l || m
STATEMENT:
1. m2 = 122° and m3 = 58°
2. 3 and 5 are supplementary angles
3. m3 + m5 = 180°
4. 58° + m5 = 180°
5. m5 = 122°
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Unit Three More Proofs for Postulates

9 and 10 Questions with Correct

Answers

True/False - Use the following figure to answer the question. When line t is perpendicular to both line l and line m, then lines l and m are parallel. - ANSWERSTrue True/False - Use the following figure to answer the question. If line t is perpendicular to both line l and line m, then angle 1 and angle 2 are both right angles. - ANSWERSTrue True/False - Use the following figure to answer the question. If lines l and m are parallel, then angle 2 and angle 3 are corresponding angles. - ANSWERSTrue True/False - Use the following figure to answer the question. If angle 1 and angle 2 are equal, then lines l and m are parallel. - ANSWERSTrue Match the reasons with the statements in the proof to prove that lines l and m are parallel, given that m∠2 = 122° and m∠3 = 58° Given: measure of angle 2 = 122° measure of angle 3 = 58° Prove: l || m STATEMENT:

  1. m∠2 = 122° and m∠3 = 58°
  2. ∠3 and ∠5 are supplementary angles
  3. m∠3 + m∠5 = 180°
  4. 58° + m∠5 = 180°
  5. m∠5 = 122°
  1. m∠2 = m∠ 5
  2. l || m - ANSWERS1. Given
  3. Exterior Sides in Opposite Rays
  4. Definition of Supplementary Angles
  5. Substitution
  6. Subtraction Property of Equality
  7. Substitution
  8. If corresponding angles are equal, then lines are parallel Match the reasons with the statements in the proof. Given: m∠6 = m∠ 8 b | | c Prove: a || b STATEMENT:
  9. m∠6 = m∠8, b||c
  10. m∠7 = m∠ 8
  11. m∠6 = m∠ 7
  12. a||b REASONS: If alternate interior angles equal, then lines ||. Substitution If lines ||, corresponding angles =. Given - ANSWERS1. Given
  13. If lines ||, corresponding angles =.
  14. If alternate interior angles equal, then lines ||.
  15. Substitution Match the reasons with the statements in the proof. Given: j || k m∠1 = m∠ 3 Prove: l || m STATEMENT:
  16. j || k, m∠3 = m∠ 1
  17. m∠1 = m∠ 2
  18. m∠2 = m∠ 3
  1. Substitution
  2. Subtraction property of equality
  3. If alternate interior angles equal, then lines are ||. In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving that lines l and m are parallel. Angles 1 and 2 are supplementary by definition. Submit the entire proof to your instructor. Given: ∠1 and ∠2 are supplementary angles Prove: l || m STATEMENT: 1.∠1 and ∠2 are supplementary angles
  4. m∠1 + m∠2 = 180°
  5. ∠1 and ∠3 are supplementary angles

  6. m∠1 + m∠2 = m∠1 + m∠ 3

  7. l || m REASON:
  8. Given

  9. Exterior sides in opposite rays



  10. ___ - ANSWERSSTATEMENT:
  11. measure of angle 1 + measure of angle 2 = 180 degrees
  12. measure of angle 2 = measure of angle 3 REASON:
  13. definition of supplementary angles
  14. definition of supplementary angles
  15. substitution
  16. subtraction
  17. If two lines are cut by a transversal so alternate interior angles are equal, then the lines are parallel (theorem 3-15)