Theorems relating lines and planes
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Theorems Relating Lines and Planes. 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?.

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Theorems Relating Lines and Planes

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Theorems relating lines and planes

Theorems Relating Lines and Planes


Review from yesterday

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

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

Theorem 2

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


Theorem 3

Theorem 3

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


Theorem 4

Theorem 4

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


Let s work on some questions

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

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


Theorems relating lines and planes

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4

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Theorems relating lines and planes

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Theorems relating lines and planes

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


Theorems relating lines and planes

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


Theorems relating lines and planes

5. If lines n 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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