Chapter 7: GEOMETRYSection 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.

Quick Review