Lesson 1-5 Postulates and Theorems Relating Points, Lines, and Planes (page 22) Essential Question How are the relationships of geometric figures used in real life situations?

The phrases, “ exactly one ” and “ one and only one ” ⇒ ____________________ and _________________________. existence uniqueness

A line contains at least _____ points; A plane contains at least _____ points not all in one line; Space contains at least _____ points not all in one plane Postulate 5

Through any two points there is exactly _____ line. 1 Postulate 6

Through any three points there is at least _____ plane ; Through any three noncollinear points there is exactly _____ plane. 1 1 Postulate 7

If _____ points are in a plane, then the line that contains the points is in that plane. 2 Postulate 8

If two planes intersect, then their intersection is a ________. line Postulate 9

THEOREMS: statements that can be ___________. proved NOTE : Writing proofs will be covered in Chapter 2.

If two lines intersect, then they intersect in exactly 1 point. Theorem 1-1 NO PROOF – for more information refer to classroom exercise #1

Through a line and a point not in the line there is exactly 1 p lane. NO PROOF - for more information refer to written exercise #20 Theorem 1-2

If two lines intersect, then exactly 1 p lane contains the lines. NO PROOF - for more information refer to postulate 5 & theorem 1-1 Theorem 1-3

Relationships between points … Two points _________ be collinear. Three points _________ be collinear or noncollinear. Three points _________ be coplanar. Three noncollinear points determine a _________. must may must plane

Relationships between points … Four points _________ be coplanar or noncoplanar. Four noncoplanar points determine ___________. Space contains at least ____ noncoplanar points. may space 4

Three ways to determine a plane … (1) 3 noncollinear points determine a plane. example:

(2)A line and a point not on the line determine a plane. example: Three ways to determine a plane …

(3) 2 intersecting lines determine a plane. example:

Relationships between two lines in the same plane … Two lines are either parallel or they ______________ in exactly one point. examples: intersect

Relationships between a line and a plane … A line and a plane are either parallel, or example:

A line and a plane are either parallel, or they _______________ in exactly one point, or example: intersect

Relationships between a line and a plane … A line and a plane are either parallel, or they _______________ in exactly one point, or the plane _______________ the line. example: intersect contains

Relationships between two planes … Two planes are either parallel or they ______________ in a line. examples: intersect

Assignment Written Exercises on page 25 WORK NOW: 3 to 11 odd numbers, GRADED: 13 to 16 ALL numbers Prepare for an open notebook test on Chapter 1: Points, Lines, Planes, and Angles How are the relationships of geometric figures used in real life situations?

Prepare for an open notebook test on Chapter 1: Points, Lines, Planes, & Angles Assignment: Chapter Review on page – 20 all numbers Chapter Test on page to 21 all numbers How are the relationships of geometric figures used in real life situations?