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Working With Geometry Lines Practice Questions

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Updated on Oct 5, 2011

Review the following concept if necessary: Working with Geometry Lines Study Guide.

Working With Geometry Lines Practice Questions

Problems

Use the following figure to answer questions 1–4.

Transversals

  1. Is line d a transversal? Why or why not?
  2. Is line y a transversal? Why or why not?
  3. Is line t a transversal? Why or why not?
  4. Is line r a transversal? Why or why not?

State whether the following statements are true or false.

  1. Perpendicular lines always form multiple right angles.
  2. The symbol "" means parallel.
  3. Transversals must always be parallel.
  4. Perpendicular lines can be formed by intersecting or nonintersecting lines.

Complete the sentences with the correct word: always, sometimes, or never.

  1. Parallel lines are ________ coplanar.
  2. Parallel lines ________ intersect.
  3. Parallel lines are ________ cut by a transversal.
  4. Lines that are skewed ________ form right angles.
  5. Skew lines are ________ coplanar.
  6. Skew lines ________ intersect.

In the following figure,m n and s t. For questions 15–18, (a) state the special name for each pair of angles (alternate interior angles, corresponding angles, or same-side interior angles), then (b) tell if the angles are congruent or supplementary.

Angles Formed by Nonparallel Lines and a Transversal

  1. 2 and 10
    1. __________
    2. __________
  2. 6 and 7
    1. __________
    2. __________
  3. 13 and 15
    1. __________
    2. __________
  4. 11 and 14
    1. __________
    2. __________
  5. List all angles that are equal to 1.
  6. List all angles that are supplementary to 11.

For questions 21–24, use the measure of the given angle to find the missing angle.

  1. m2 = 100°, so m7 = _____
  2. m8 = 71°, so m12 = _____
  3. m5 = 110°, so m7 = _____
  4. m2 = 125°, so m11 =_____

Complete the statement for practice problems 25–30.

  1. Alternate interior angles are similar to corresponding angles because ____________________.
  2. Alternate interior angles differ from corresponding angles because ____________________.
  3. Same-side interior angles are similar to alternate interior angles because ____________________.
  4. Same-side interior angles differ from alternate interior angles because ____________________.
  5. Same-side interior angles are similar to corresponding angles because ____________________.
  6. Same-side interior angles differ from corresponding angles because ____________________.

Answers

  1. Yes; line d cuts across lines t and r.
  2. Yes; line y cuts across lines t and r.
  3. No; line t intersects lines d and y at the same point, not two different points.
  4. Yes; line r cuts across lines d and y at two different points.
  5. true
  6. False; the symbol means perpendicular.
  7. False; transversals can be perpendicular, but they do not have to be perpendicular.
  8. false
  9. always
  10. never
  11. sometimes
  12. never
  13. never
  14. never
  15. corresponding angles; congruent
  16. same-side interior angles; supplementary
  17. corresponding angles; congruent
  18. alternate interior angles; congruent
  19. 3, 6, 8, 9, 11, 14, and 16
  20. 2, 4, 5, 7, 10, 12, 13, and 15
  21. 80°
  22. 109°
  23. 110°
  24. 55°
  25. They are both pairs of congruent angles when formed by parallel lines and a transversal.
  26. Alternate interior angles are both "inside" the parallel lines. Corresponding angles are a pair of angles with one angle "inside" the parallel lines and one "outside" the parallel lines.
  27. They are both pairs of interior angles.
  28. Same-side interior angles are supplementary. Alternate interior angles are congruent.
  29. Both pairs of angles are on the same side of the transversal.
  30. Same-side interior angles are supplementary. Corresponding angles are congruent. Also, both same-side interior angles are interior while corresponding angles have one angle "inside" and one "outside" the parallel lines.
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