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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?.

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Theorems Relating Lines and Planes

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  1. Theorems Relating Lines and Planes

  2. 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

  3. 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.

  4. Theorem 2 • Through a given point there passes one and only one plane perpendicular to a given line.

  5. Theorem 3 • Through a given point there passes one and only one line perpendicular to a given plane.

  6. Theorem 4 • If two planes are perpendicular to the same line, they are parallel.

  7. 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

  8. 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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  10. 2 4

  11. 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

  12. 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

  13. 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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