Geometry 2.3 Postulates and Diagrams

Use the diagram to determine whether you can assume the statement.

Groups:

(a) Yes, I can assume.

,

(b) No, I can't assume.

• Points U, M, and O are coplanar

Your friend claims that if three lines intersect each other, then there are two points of intersection because of the Line Intersection Postulate. Is your friend correct? Why or why not?

• Yes, 3 lines will have 2 points of intersection

• Yes, because that's true

• No, 3 lines can interest each other at 1 or 3 points

• No, 3 lines can't all intersect each other

Match the following postulates with their correct example using the diagram.

• one line containing points C and H

• Three Point Postulate

• B, H, E are noncollinear & define planeM

• Line Intersection Postulate

• Two Point Postulate

• line l contains points G and D

• Plane-Point Postulate

• Plane M contains points B, H, and E

• Line-Point Postulate

What postulate would be represented by:

Points G and E line in Plane M, so GE lies in plane M.

• Two Point Postulate

• Line Intersection Postulate

• Plane Point Postulate

• Plane Line Postulate

Rewrite the Three Point Postulate in if-then form.

If ​ (a)   , then ​ (b)  

• three points are noncollinear
• there exists exactly one plane that contains them.
• there are two noncollinear points
• there intersection is exactly one point