Chapter 7: GEOMETRY Section 1 Lines and Planes. California Standards  Measurement and Geometry 2.0:  Identify and describe the properties of two- dimensional.

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Presentation transcript:

Chapter 7: GEOMETRY Section 1 Lines and Planes

California Standards  Measurement and Geometry 2.0:  Identify and describe the properties of two- dimensional figures.  Mathematical Reasoning 1.1:  Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information and observing patterns.

Key Vocabulary  PLANE: -A FLAT surface that extends INDEFINITELY in ALL directions.  POINT: -A POINT is a fixed location. A POINT has NO size. -A POINT is ALWAYS identified by a CAPITAL letter.  LINE: -A LINE is a series of POINTS that extend in OPPOSITE directions without end. -This means BOTH sides of the LINE continue on INFINITELY in each respective direction. -You name a LINE by ANY two POINTS on the line OR by a lowercase letter.  RAY:-A RAY is a part of a LINE with ONE endpoint and ALL the points of the line on one side of the endpoint.  SEGMENT:-A SEGMENT is part of a LINE with TWO endpoints and ALL points in between.  INTERSECTING LINES: Intersecting lines are lines that cross at ONE common point.  PARALLEL LINES: Parallel lines are lines that run side by side and NEVER cross.  SKEW LINES: Skew lines lie in DIFFERENT planes. -They are NEITHER Parallel NOR Intersecting.

NAMING SEGMENTS, RAYS and LINES  To name a SEGMENT, remember you need to find TWO ENDPOINTS.  The ENDPOINTS effectively “TRAP” the other points within the line and allow for you to call out the SEGMENT by the ENDPOINTS themselves.  A straight bar over the TWO Endpoints is how you write it out.  To name a RAY, you need to first find ONE ENDPOINT.  Then imagine that you are shooting a “RAY” gun in one direction, catching ALL of the points that fall along its path.  You name the RAY by starting with the ENDPOINT and then naming another POINT along the one-way path.  A One-way arrow is placed over the TWO Endpoints is how you write it out.  To name a LINE, you simply need to find TWO points on a straight line path and extend them in BOTH directions, INFINITELY.  A double arrowed bar placed over TWO Endpoints is how you write it out.

INTERSECTING, PARALLEL, and SKEW  INTERSECTING:  An easy way to remember INTERSECTING lines is CRISS CROSS.  Intersecting lines CRISS CROSS and form an X.  Where the X is located is your Point of Intersection.  PARALLEL:  An easy way to remember PARALLEL lines is Railroad Tracks.  Railroad Tracks NEVER cross.  Side by side paths run NEXT to each other NEVER touching or crossing.  SKEW:  Skew lines line in DIFFERENT planes of existence.  The planes NEVER Intersect NOR are they Parallel to each other.

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