 Give an example of a point, line and plane that can be found in the classroom.

Geometry Online Textbook

 Known words used to describe a new word Undefined terms – not formally defined There are 3 in geometry. Point LinePlane

1. Has no dimension (no length, width, thickness) 2. Usually represented by a dot 3. Named using one capital letter, B

Extends forever in one dimension (length) Has an arrowhead on each end representing the fact that it goes on forever Consists of an infinite amount of points Always straight Named with a lowercase script letter or by 2 points on the line A B l Can be called: Line l Line AB or AB Line BA or BA

Extends forever in 2 dimensions (length & width) A flat surface consisting of infinitely many points Usually represented by a 4-sided figure Named with a capital script letter or 3 points on the surface of the plane A B C W Can be named: Plane W Plane ABC, plane BCA, plane CBA, etc.

 Collinear points – points that lie on the same line  Coplanar points – points that lie on the same plane  Space – a boundless, three-dimensional set of all points. Space can contain lines and planes.

 POINT  LINE  PLANE  COLLINEAR POINTS  NONCOLLINEAR POINTS  COPLANAR POINTS  NONCOPLANAR POINTS

 Practice Practice

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A section of a line that has 2 endpoints Named by its endpoints. AB or BA The length or measure of AB is written as AB. AB

AB

If B is between A & C, then AB + BC = AC. If AB + BC = AC, then B is between A & C.

Find the value of the variable and LM if L is between N and M. 1. NL = 5x, LM = 3x, and NL = NL = 6x – 5, LM = 2x + 3, and NM = 30

 Two segments having the same measure are congruent.   is read is congruent to. (Red slashes indicate t he segments are congruent.)2 cm

 Handout Handout  Homework Page – 39 all

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Practice

NUMBER LINECOORDINATE PLANE  PQ = | b – a | or | a – b |  Example Find the distance between the two points -5 and 1.  The distance between d between two points with coordinates (x 2 - x 1 ) and (y 2 – y 1 ) is given by d = √ (x 2 – x 1 ) 2 + (y 2 – y 1 ) 2  Example Find the distance between R(5.1) and S(-3,-3).

 Used for finding the coordinates of the midpoint of a segment in a coordinate plane.  If the endpoints are (x 1,y 1 ) & (x 2,y 2 ), then

Ex: Find the midpoint of SP if S(-3,-5) & P(5,11

Ex: The midpoint of AB is M(2,4). One endpoint is A(-1,7). Find the coordinates of B.

 Handout Handout  Homework Page all; all; all  Quiz next block on Sections 1-1 to 1-3  You must know the Distance and Midpoint Formulas  Study!!!!

Geometry Online Textbook User Name: GEOVA05 Password: crAju4re

Practice

 2 rays that share the same endpoint (or initial point) Y Z X Sides – the rays XY & XZ Vertex – the common endpoint; X Named <YXZ, <ZXY (vertex is always in the middle), or <X (if it’s the only <X in the diagram). Angles can also be named by a #. (<5) 5

A B C D <B ?

 m<A means the “measure of <A”  Measure angles with a protractor.  Units of angle measurement are degrees ( o ).  Angles with the same measure are congruent angles.  If m<A = m<B, then <A  <B.

 B is ___________  C is ___________  D is ___________ in the interior in the exterior on the < A B C D

 Acute angle –  Right angle –  Obtuse angle –  Straight angle – Measures between 0 o & 90 o Measures exactly 90 o Measures between 90 o & 180 o Measures exactly 180 o

 Piece of a line with only one endpoint (initial point) and continues forever in the other direction  Named by the endpoint and a second point named on the ray. (name MUST begin with the endpoint!) AB A B

 2 rays that share a common initial point and face opposite directions.  QP and QS are opposite rays. PQS

Angles that have the same measure are congruent angles. Arcs on the figure also indicate which angles are congruent.

 Practice Practice

 Draw & label points A & B.  Draw & label points C & D.  Draw AB.  Draw BC.  Draw AC.  Draw DA.

 Intersect – 2 or more figures intersect if they have one or more points in common.  Intersection – all points or sets of points the figures have in common  What is the intersection of: AB & DA BC & AC BC & BC