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Theorems Relating Lines and PlanesPowerPoint Presentation

Theorems Relating Lines and Planes

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Review From Yesterday

- What is the difference between collinear points and coplanar lines?
- What happens when two planes intersect?
- What are the 4 ways you can create a plane?

- Answer: collinear points are points on the same line and coplanar lines are lines in the same plane

- Answer: ONE line is formed

- Answer: 3 noncollinear points, a line and a point off

the line, two intersecting lines, two parallel lines

Theorem 1

- If a line is perpendicular to each of two intersecting lines at their point of intersection, then the line is perpendicular to the plane determined by them.

Theorem 2

- Through a given point there passes one and only one plane perpendicular to a given line.

Theorem 3

- Through a given point there passes one and only one line perpendicular to a given plane.

Theorem 4

- If two planes are perpendicular to the same line, they are parallel.

Let’s work on Some Questions

- A line perpendicular to a plane is perpendicular to every line in the plane. True of False?
- Answer: False

• Through a point outside a plane, one

and only one plane can be drawn

perpendicular to the plane. True or False?

Answer: False

More Practice!

- Fill in the blank: Two planes that are perpendicular to the same line are _____________ to each other
- Answer: parallel

- Two lines _____________ to the same plane are parallel.
- Answer: Perpendicular

4

1. Line k is drawn so that it is perpendicular to two distinct planes, P and R. What must be true about planes P and R?

(2) Planes P and R are parallel.

- Lines and intersect at point E. Line m is perpendicular to lines and
- at point E.
- Which statement is always true?

(3) Line m is perpendicular to the plane

3. For this rectangular solid, Planes EGH and GAB intersect to form line

4. One dihedral angle formed by planes l and q is:

P – YZ – A

5. If lines to form linen and m are each perpendicular to plane A, what is the relationship between n and m ?

n and m are coplanar

6. What happens when two planes intersect? ________________________________

One line is formed

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