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Theorems Relating Lines and Planes
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Review From Yesterday - Answer: ONE line is formed
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
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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.
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Theorem 2 Through a given point there passes one and only one plane perpendicular to a given line.
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Theorem 3 Through a given point there passes one and only one line perpendicular to a given plane.
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Theorem 4 If two planes are perpendicular to the same line, they are parallel.
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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
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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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2 4
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(2) Planes P and R are parallel.
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
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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
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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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