Postulates of Euclidean Geometry & Santucci’s Starter When lines intersect, they intersect at a point. If n lines intersect, they must intersect in a minimum of one point (see below). Use inductive reasoning to find a formula for the maximum number of intersection points when n lines intersect. Work with one partner. Minimum # intersection points = 1 # lines# intersection points ? 4 ? … n ?

When done with starter… 1. Peer edit homework vs. key (check odds in back) Request problems on the board When done: Pick up Postulates activity.

Postulates of Euclidean Geometry activity Groups Use your book or interactive text Record all postulates in your notebook.

A postulate, or axiom, is an accepted statement of fact. 1. Through any 2 points there is exactly 1 line. 2. If 2 lines intersect they intersect in exactly 1 point. 3. If 2 planes intersect they intersect in exactly 1 line 4. There is exactly 1 plane through any 3 noncollinear points

Pairs Sketch: 1. 3 collinear points coplanar points that are noncollinear. 3. The intersection of two planes. 4. Two line segments who do not intersect but whose endpoints are noncollinear.

New Pairs check & describe 1.Choose 3 “points” in the room and describe the plane that could be drawn through them. 2. Describe 2 parallel lines found in the room. 3. Describe 2 parallel planes found in the room. 4. Describe 2 skew lines found in the room.

HW Answers: pp #33-36, 48, 49 evens 34: No, a ray has only ONE endpoint 36: Check vs. your neighbor 48: C could be (0,0). Slope must be 3/2, with equation y = (3/2) x