1-2: Points, Lines and Planes

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Presentation transcript:

1-2: Points, Lines and Planes

l Undefined Terms P ABC Term Description Name Diagram Point Indicates location One capital letter Has no size Line Straight path Any two points: Extends in opposite directions or Has no thickness One lowercase letter: Infinitely many points l Flat surface One uppercase letter: Plane Extends without end P Has no thickness Three points not on same line: Infinitely many lines ABC

Types of Points Collinear: Coplanar: Space: Two or more points that lie on the same line Coplanar: Three or more points that lie on the same plane Lines on the same plane are coplanar Space: Set of all points in three dimensions. A B C C A B D

Example 1: What are two other ways name ? What are two ways to name plane Q? What are the names of three collinear points? What are the names of four coplanar points? line l or plane AEC plane ADC points A, E, D points A, F, B points A, E, C points A, E, B Complete Got It? #1 p.12 b. plane RVS c. N, Q, T

Defined Terms Term Description Name Diagram Segment Part of a line Two endpoints: Two endpoints and all points between or Ray Part of a line Endpoint and any point on the ray: One endpoint and all points on the line on one side of endpoint Opposite Ray Two rays that share the same endpoint Shared endpoint and any other point on each ray: Form a line

Example 2: What are the names of the segments in the figure? What are the names of the rays in the figure? Which of the rays in part(b) are opposite rays? Complete Got It? #2 p.13

Postulates (statements assumed to be true) Through any two points there is exactly one line. Postulate 1-2 If two distinct lines intersect, then they intersect in exactly one point. Postulate 1-3 If two distinct planes intersect, then they intersect in exactly one line. A B C D A B G

Example 3: What is the intersection of and ? What is the intersection of plane ABCD and ? What is the intersection of plane ABGH and plane DCHG? G A Complete Got It? #3 p.14 a. plane BFE b. Two planes intersect in one line, so you need two common points to name the common line.

Postulate Postulate 1-4 Through any three noncollinear points there is exactly one plane. C A B D

Example 4: Each surface of the box represents part of a plane Which plane contains points A, B and C? Which plane contains points E, H and C? plane ABCD plane EHCB a. plane LMNP b. Complete Got It? #4 p.15

Homework: P. 16-17, #’s 8-22, 40-45