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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