1. Move points E, F, and G so they are [b]coplanar[/b] (lie on plane [i]A[/i]). Planes are determined by three points (points are determined by one, and lines by two!). Plane [i]A[/i] has dotted "edges" because it extends infinitely in all directions! Think of a plane as a floor that extends infinitely.[br]2. Move point H so it lies outside of plane A.[br]3. Move the line so it contains point H and intersects the plane at point F. Points H and F are [b]collinear [/b]because they lie on the same line ([math]\longleftrightarrow HF[/math]).[br]3. Move the line segment to create line segment [math]\overline{EF}[/math].[br]4. Move the ray to create ray [math]\longrightarrow GK[/math].[br]
Take a few minutes to mess around with the toolbar below. Create a point, draw a line, make a triangle, draw a picture! Have fun! Then answer the following question:[br][br]There are three cases of relations ("intersections") between two lines. What are they? Show one case using the toolbox below! Remember that a line is determined by two points, so start by adding two points before drawing a line between them.
Two lines can intersect in one point, be the same line, or not intersect at all (lines are parallel)!
1. In the image below, where does line [math]\longleftrightarrow ED[/math] intersect plane [i]P[/i]?
2. Where does line [math]\longleftrightarrow ED[/math] intersect plane [i]P[/i]?
It doesn't! The plane and line are parallel, so they never intersect.
1. Where does plane [i]A [/i]intersect with plane [i]B[/i]?
Line [i]k [br][/i]Line [math]\longleftrightarrow GH[/math]
2. There are two other cases of relations between two planes. What are they? [Hint: Think about two pieces of paper with "edges" that extend infinitely in all four directions of the paper.]
Two planes can be parallel (never intersect) or they can be the same plane!
3. When will the 2 parallel planes intersect?
if they are the same plane