1.1Points, Lies, and Planes Warm Up Simplify Each Expression. 3x – 5 + 7x 2. 5y – 12y + 8 3. 4(x – 3) – 24 4. -8m + 6(2m – 12) 5. 3(2p – 8) – 4(8p – 7)

1.1Points, Lies, and Planes Objectives Identify, name, and draw points, lines, segments, rays, and planes. Apply basic facts about points, lines, and planes.

Definition – Uses __________ words to describe a ________ word.

Three Undefined Terms Description Point has _____ dimension. It is usually represented by a _______ ________ Line extends in _____ dimension. It is usually represented by a straight line with two arrowheads to indicate that the line extends without end in ______ ___________ Plane extends in _____ dimensions. It is usually represented by a shape that looks like a tabletop or wall. Your must imagine that the plane extends __________ _____, even though the drawing of a plane appears to have edges. Name Picture  

Description Collinear points are ________ that lie on the same _________. Coplanar points are __________ that lie on the same ____________. Picture  

Example 1 Name a point Name a line Name a plane Name three points that are collinear. Name three points that are not collinear Name four points that are coplanar Name four points that are not coplanar

Between a point is between two other points if the three points are _______________. Intersect – to have one or more __________ in common. Intersection - the set of ___________ that two or more geometric figures have in ___________.

Description Line Segment (Segment) Part of a line that consists of ______ points, called endpoints, and all points on the line that are between the ________________.   Ray Part of a line that consists of a ________, called an initial point, and all points on the line that extend in _______ direction. Opposite Rays If C is ___________ A and B, then 𝐶𝐴 and 𝐶𝐵 are opposite rays. Name Picture

c. Name the intersection of plane N and plane T. Example 2 Name two opposite rays. b. Name a point on 𝐵𝐶 . c. Name the intersection of plane N and plane T.

Example 3 Draw three noncollinear points, J, K, L. Then draw 𝐽𝐾 , 𝐾𝐿 , and 𝐿𝐽 . b. opposite rays with a common endpoint T. c. 𝑄𝑅 and 𝑆𝑇 that intersect at point M.

Example 4 Draw and label each of the following. a figure that shows a line that lies in a plane. b. a figure that shows 𝐴𝐵 intersect plane S at point C.

Line Pairs Description Parallel lines – ____________ lines that do not ______________ Perpendicular Lines – two lines that ____________ to form ____________ angles. Intersecting Lines – Lines that _________. Skew Lines - ______ ____________ lines that do not _______________ Name   Picture

Example 5 Identify each of the following. a. a pair of parallel segment b. a pair of skew segments a pair of perpendicular segments What do you notice about all of the intersecting lines in this picture?   Draw a new picture where this is not true.