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geometry in 3D

geometry in 3D. Honors Geometry. Planes. How many lines can be passed through one point? How many planes can be passed through one point? How many planes can be passed through two distinct points? Is it possible to have more than one line intersecting a plane at one point?

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geometry in 3D

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  1. geometry in 3D Honors Geometry

  2. Planes • How many lines can be passed through one point? • How many planes can be passed through one point? • How many planes can be passed through two distinct points? • Is it possible to have more than one line intersecting a plane at one point? • How many planes can intersect a line at one point?

  3. Planes • How many lines can be passed through one point? INFINITELY MANY • How many planes can be passed through one point? INFINITELY MANY • How many planes can be passed through two distinct points? INFINITELY MANY • Is it possible to have more than one line intersecting a plane at one point? YES • How many planes can intersect a line at one point? INFINITELY MANY

  4. Planes • Is it possible for two planes to meet in just one point? • Can two planes contain the same line? • Can three planes meet in just one point? • If three points do not lie on the same line, how many different planes can contain those three points? • The intersection of a line and a plane is a: • The intersection of two planes is a:

  5. Planes • Is it possible for two planes to meet in just one point? NO • Can two planes contain the same line? YES • Can three planes meet in just one point? YES • If three points do not lie on the same line, how many different planes can contain those three points? ONE • The intersection of a line and a plane is a: POINT • The intersection of two planes is a: LINE

  6. Planes • True or false: Two lines are parallel if they do not intersect. • True or false: If two distinct lines are perpendicular to a third line, then they are parallel.

  7. Planes • True or false: Two lines are parallel if they do not intersect. FALSE (could be skew… statement is true in a plane only – 2D) • True or false: If two distinct lines are perpendicular to a third line, then they are parallel. FALSE (true in 2D on a plane, but not in 3D)

  8. Four Methods to Determine a Plane • Three non-collinear points • A line and a point not on that line • Two intersecting lines • Two parallel lines

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