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### 1.1

1. 1. 1.1 Identify Points, Lines, and Planes Objective:  Name and sketch geometric figures.CA Standards: 1 Mr. Tagle-Nava 1
2. 2. VocabularyIn geometry, the terms point, line, and plane are accepted as intuitive ideas and are not defined. These undefined terms are then used in the definitions of other terms. A point AA point can be represented by a dot, but it does not have any size or mass.A line is made of points and extents j in two directions. S T line j ST TS Mr. Tagle-Nava 2
3. 3. VocabularyA plane is a flat surface that extends A Plane P without ending and has no B P c thickness. Plane ABCCollinear Points are all points in one line. ACoplanar Points are points all in one B plane. P c Mr. Tagle-Nava 3
4. 4. VocabularyDefined Terms that can be described using known Terms words.Line segment or segment AB consists of the endpoint A and B. A B AB BAThe ray AB consists of the Initial Point A and all the points that lie A B on the same side of A as point B. AB Mr. Tagle-Nava 4
5. 5. VocabularyOpposite Rays If C is between A and B,    A C B then CA and CB are opposites rays.Intersection The intersection of two figures is the set of points that are in both figures. Mr. Tagle-Nava 5
6. 6. Undefined TermsPoint A point has no dimension. It is represented by a dot.Line A line has one dimension. It is represented by a line with two arrowheads, but extends without end.Through any two points, there is exactly one line. You can use any two points on a line to name it.Plane A plane has two dimensions. It is represented by a shape that looks like a floor or wall, but it extends without end.Through any three points not on the same line, there is exactly one plane. You can use three points that are not all on the same line to name a plane. Mr. Tagle-Nava 6
7. 7. Example 1  Give two other names for LN.Given another name for plane Z.   Other names for LN are LM and line b.Other names for plane Z are plane LMP and LNP. Name three points that are collinear. Name four points that are coplanar. Points L, M, and N lie on the same line, so they are collinear. Points L, M, N, and P lie on the same plane, so they are coplanar. Mr. Tagle-Nava 7
8. 8. Give two other names for VX. 1. X, Y 2. WX, XW 3. WX, XW Mr. Tagle-Nava 8
9. 9. Defined Terms Line AB (written as AB) and points A and Bare used here to define the terms below.Segment The line segment AB, or segment AB,(written as AB) consists of the endpoints A and B   and all points on AB that between A and B.Note that AB can also be named BA  Ray The ray AB, (written as AB) consists of the endpoint A  and all points on AB that lie on the same side of A as B.    Note that AB and BA are different. Mr. Tagle-Nava 9
10. 10. Example 2Give two other names for VX. Another name for VX is XV.Name all rays with endpoints W.Which of these rays are opposite rays?        The rays with endpoint W are WV, WY, WX, and WX.        The opposite rays with endpoint W are WV and WX, WY, and WZ. Mr. Tagle-Nava 10
11. 11. Example 3Sketch a plane and a Sketch a plane and a line that intersects the line that is in the plane at more than plane. Sketch another one point. line that intersects the line and plane at a point. Mr. Tagle-Nava 11
12. 12. Example 4Draw two planes that intersect in a line.Step 1Draw one plane as if you are facing it.Step 2Draw a second plane that is horizontal.Use dashed lines to show where one plane is hidden.Step 3 Draw the line of intersection. Mr. Tagle-Nava 12
13. 13. Name the intersection of MX and line a. 1. X, Y 33% 33% 33% 2. c 3. M 1 2 3 Mr. Tagle-Nava 13
14. 14. Homework 5 (2 – 32, E)12 (2 – 30, E)19 (2 – 32, E)28 (2 – 42, E)38 (2 – 32, E)44 (2 – 30, E)52 (2 – 34, E)60 (2 – 34, E)Mr. Tagle-Nava 14