Euclid. Father of Geometry Euclidean Geometry Euclid s Elements

Transcription

1 Euclid Father of Geometry Euclidean Geometry Euclid s Elements

2 Point Description Indicates a location and has no size. How to Name it You can represent a point by a dot and name it by a capital letter. Name A

3 Line Description Represented by a straight path that extends in two opposite directions without end and has no thickness. A line contains infinitely many points. Sketch Name l How to Name it You can name a line by any two points on the line or by a single lower case cursive letter. AB AC BC BA CA CB line l

4 AB BA Naming Lines Examples

5 Plane Description Represented by a flat surface that extends without end and has no thickness. A plane contains infinitely many lines. How to Name it A single capital letter such as plane P or 3 points in the plane that do not all lie on the same line such as plane ABC. Name plane P Plane ABC Plane ACB Plane BAC Plane BCA plane CAB Plane CBA

6 Naming a Plane Examples Name plane ABC plane ACB plane ABD plane ADB plane ACD plane ADC plane R plane BAC plane CAB plane DAB plane BCA plane CBA plane DBA plane BAD plane CAD plane DAC plane BDA plane CDA plane DCA plane BCD plane CBD plane DBC plane BDC plane CDB plane DCB

7 Point, Line and Plane Known as: The Building Blocks of Geometry The Undefined Terms

8 Collinear Points Definition Points that lie on the same line. A B C How to Name it Since they are points, you name them as you would a normal point with a single capital letter. Name A BC D (each individual point)

9 Coplanar Points Definition Points that lie in the same plane. A B C How to Name it So you name them with the same rules as POINTS. Name A B C

10 Coplanar Lines Definition Lines that lie in the same plane. D F E G How to Name it So you name them with the same rules as LINES. Name AB or BA CD or DC EF or FE

11 Segment or Line Segment Definition Part of a line that consists of two endpoints and all points between them. How to Name it By its two endpoints (only 2 letters). Name AB or BA

12 Line Segment Example AB or BA AD or DA

13 Ray Definition Part of a line that contains one endpoint and all the points of the line on one side of the endpoint. How to Name it By the endpoint and another point on the ray. Name

14 Naming Ray Examples

15 Opposite Rays Definition Two rays that share the same endpoint and form a line. Name How to Name it By the shared endpoint and any other point on each ray.

16 Space Definition Set of all points in three dimensions. *No sketch*

17 Congruent Segments Definition Segments that have the same length NUMBERS are equal (=), THINGS are congruent ( ) means is congruent to

18 IMPORTANT!!!!! mab is read as: The measure of segment AB This is a number This could be equal to another number AB is read as: segment AB this is an object This is only congruent to another object, NEVER equal. AB (the book uses this often) is read as the distance from point A to point B This is a number This could be equal to another number

19 IMPORTANT!!!!! In a statement to indicate that two segments are congruent we use the congruency symbol In a sketch or drawing we use tick marks of the same number to indicate congruent segments

20 Midpoint Definition A point that divides a segment into two congruent segments Note: On a sketch you MUST have the congruency tick marks.

21 Segment Bisector Definition A line, segment, ray or plane that intersects a segment at its midpoint Note: On a sketch you MUST have the congruency tick marks.

22 Angle Definition Formed by two rays with the same endpoint. How to Name it By the vertex 3 letters (one from each ray and the vertex) with the vertex as the middle letter A number Name A BAC CAB 1

23 Important: Naming an Angle

24 Naming Angle Examples A B 1 C E GEO OEG 3 Other names for 3: ABD DBA Other names for 4: DBC CBD Other names For BIG angle: ABC CBA

25 Straight Angle Definition Angle whose measure is 180. A B C Note: You do not need a degree measure but be sure it looks like a line. Name B ABC CBA