Theorems Relating Lines and Planes
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Transcript of Theorems Relating Lines and Planes
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?
– 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
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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.
2. Lines and intersect at point E. Line m is perpendicular to lines and
at point E.
Which statement is always true?
k1k2
(3) Line m is perpendicular to the plane
3. For this rectangular solid, Planes EGH and GAB intersect to form line
GH
4. One dihedral angle formed by planes l and q is:
P – YZ – A
5. If lines n and m are each perpendicular to plane A, what is the relationship between n and m ?
6. What happens when two planes intersect? ________________________________
n and m are coplanar
One line is formed