Concept Byte: Perpendicular Lines and Planes

Use With Lesson 3-4

ACTIVITY

As you saw in Chapter 1, you can use a polygon to represent a plane in space. You can sketch overlapping polygons to suggest how two perpendicular planes intersect in a line.

Activity

Draw perpendicular planes A and B intersecting in C D ↔ . modified c d with left right arrow above , .

Step 1 Draw plane A and C D ↔ modified c d with left right arrow above  in plane A.

Step 2 Draw two segments that are perpendicular to C D ↔ . modified c d with left right arrow above , .  One segment should pass through point C. The other segment should pass through point D. The segments represent two lines in plane B that are perpendicular to plane A.

Step 3 Connect the segment endpoints to draw plane B. Plane B is perpendicular to plane A because plane B contains lines perpendicular to plane A.

Exercises

1. Draw a plane in space. Then draw two lines that are in the plane and intersect at point A. Draw a third line that is perpendicular to each of the two lines at point A. What is the relationship between the third line and the plane?
2. 1. Draw a plane and a point in the plane. Draw a line perpendicular to the plane at that point. Can you draw more than one perpendicular line?
   2. Draw a line and a point on the line. Draw a plane that is perpendicular to the line at that point. Can you draw more than one perpendicular plane?
3. Draw two planes perpendicular to the same line. What is the relationship between the planes?
4. Draw line l through plane P at point A, so that line l is perpendicular to plane P.
   1. Draw line m perpendicular to line l at point A. How do m and plane P relate? Does this relationship hold true for every line perpendicular to line l at point A?
   2. Draw a plane Q that contains line l. How do planes P and Q relate? Does this relationship hold true for every plane Q that contains line l?

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