2-5 Postulates and Paragraph Proofs Postulate or Axiom: A statement that is accepted as true Postulate 2.1: Through any two points, there is exactly one line. Postulate 2.2: Through any three points not on the same line, there is exactly one plane.

Example #1 Review Example #1 on page 105 and then complete the following example… Some snow crystals are shaped like regular hexagons. How many lines must be drawn to interconnect all vertices of a hexagonal snow crystal? Answer: 15

More Postulates Postulate 2.3: A line contains at least two points. Postulate 2.4: A plane contains at least three points not on the same line. Postulate 2.5: If two points lie in a plane, then the entire line containing those points lies in that plane. Postulate 2.6: If two lines intersect, then their intersection is exactly one point. Postulate 2.7: If two planes intersect, then their intersection is a line.

Example #2 Determine whether each statement is always, sometimes, or never true. Explain. 1) If points A, B, and C lie in plane M, then they are collinear. Sometimes 2) There are at least two lines through points M and N. Never 3) If two coplanar lines intersect, then the point of intersection lies in the same plane as the two lines. Always 4) GH contains three noncollinear points.

Paragraph Proofs Theorem: A statement or conjecture that has been shown or proven to be true. Proof: A logical argument in which each statement you make is supported by a statement that is accepted as true. Paragraph Proof (informal proof): One type of proof.

5 essential parts of a good proof 1) State the theorem or conjecture to be proven 2) List the given information 3) If possible, draw a diagram to illustrate the given information 4) State what is to be proved 5) Develop a system of deductive reasoning

Example #3 Given that , and C is between A and B, write a paragraph proof to show that C is the midpoint of AB. A C B Midpoint Theorem If M is the midpoint of AB, then

Homework #13 p. 108 8-21, 28-29 Quiz Monday