Construct a Parallel Line

In this Gizmotm, you will construct a line parallel to a given line, through a point not on the line.

  1. In the Gizmo, with Construct a parallel line selected, observe the screen and follow the directions given to the left. After you complete each step, click Continue to go on to the next step of the construction. At any time, if you wish to see the overall strategy for this construction, click How?. If you need help understanding the purpose of a particular step, click Why?. If you want to start over on the construction, click Reset. As you work through the construction, answer the questions below.
    1. At the beginning of construction step 4, two new points appear on the diagram, points P and Q. What is the relationship of those points to point H?
    2. In construction step 6, it is important to keep the opening of the compass the same as it was in step 5. Explain why.
  2. Complete the construction using the Gizmo.
    1. What two lines are parallel?
    2. What angles did you construct to be congruent? Click on Click to measure angles and use the interactive protractors to verify that these angles are congruent. (For help using the protractor, click on Gizmo help, below the Gizmo.)
    3. Explain how those congruent angles guarantee that the lines are parallel.

Construct a Perpendicular Line

In this section, you will construct a line perpendicular to a given line, through a point on the line.

  1. Turn off the protractors and select Construct a perpendicular line. Observe the screen and follow the directions given to the left. As you work through the construction, answer the questions below.
    1. At the beginning of construction step 2, points R and S appear on the diagram. What is the relationship of points R and S to N?
    2. In construction step 2, when you place the compass center on R, try making the compass radius very small. Click Continue. What does the Gizmo feedback tell you? Why is it important to make the radius greater than the distance from R to N? (Hint: you may need to complete the construction to see why this is important.)
  2. Complete the construction using the Gizmo.
    1. Which two lines are perpendicular? Verify this with the protractors.
    2. What is the relationship of point T to points R and S? Click on Click to measure lengths and verify this using the interactive rulers. (For help using the ruler, click on Gizmo help, below the Gizmo.)
    3. Explain how the relationship of point T to points R and S guarantees that these lines are perpendicular.