2. Section 1-2: Points, Lines, and Planes SPI 32A: Identify properties of plane figures Objectives: Understand basic terms of geometry A part of mathematics concerned with questions of size, shape, relative position of figures and with properties of space. One of the oldest sciences initially used and studied in Ancient Mesopotamia & Egypt.

3. Euclidean Geometry Definitions Axioms or Postulates Accepted statement or fact Theorems Statement deduced from axioms which has been proven to be true

4. How to sketch: How to label: * Use capital printed letters. * dots A B C A * Never label two points with the same name (in the same sketch). Definition: Designates a specific location Has no size Named by a capital letter A B

5. Co--: together Linear: line Collinear points are points that lie on the same line. (The line does not have to be visible.) non-collinearcollinear Definition:

6. Any other set of three points do not lie on a line, so no other set of three points is collinear. For example, X, Y, and Z and X, W, and Z form triangles and are not collinear. In the figure below, name three points that are collinear and three points that are not collinear. Points Y, Z, and W lie on a line, so they are collinear. Identify Collinear and Non-collinear Points

7. A set of all points A geometric figure is a set of all points

8. How to sketch: How to label: 1- small “script” letter * must have arrows at both ends 2- any two points on the line (Two methods) n Possible Names: ? ? ? ? ? ? Definition: Series of points that extends in 2 opposite directions without end Line n

9. Flat surface with no thickness Contains many lines Extends indefinitely Named by a single capital letter or by at least 3 of its noncollinear points P A B C Plane PPlane ABC Coplanar: Points, rays, segments, lines, etc... located in the same plane m G NonCoplanar: Not in the same plane

10. How to sketch: How to label: * horizontal * vertical 1- capital “script” letter 2- any three points on the plane (Two methods) * other horizontal “edges” vertical “edges” M P N

11. How to label: any three (or more) points on the plane How many planes do you see? plane ABCD plane ABC plane BCD plane CDA plane DAB etc. Investigate Planes

12. How to label: any three (or more) points on the plane How many planes do you see? plane AEHD plane EHD plane HDA plane DAE plane AEH etc. Investigate Planes

13. How to label: any three (or more) points on the plane How many planes do you see? plane ABFE plane ABF plane BFE plane FEA plane EAB etc. Investigate Planes

14. How to label: any three (or more) points on the plane Any three points determine a plane! plane AGF plane BDG etc. plane AFGD plane ACGE plane ACH Investigate Planes

15. Coplanar objects (points or lines) are objects that lie on the same plane. (The plane does not have to be visible.) Definition: Are they coplanar? ABC ? yes ABCF ? NO HGFE ? yes EHCB ? yes AGF ? yes CBFH ? NO Investigate Planes

16. Group Work Instructions 1. Quiet Signal: Teacher raises hand and students raise. their hand to help signal others to be quiet and listen. 2. Group Formation: Shoulder partners (A and B) and face partners. 3. Stay on task and work together. 4. Use a small voice. 5. Use stop and go card only if no one in your group can help with the problem. 6. Praise each other by saying “Good Job” and high five. Structure: Rally Coach 1. Partner A solves the 1st problem by writing or constructing and talking through the solution. 2. Partner B watches, listens, coaches, and praises. 3. Student A and B then switch roles. 4. Repeat process until activity is complete.

17. Construct a net and Label a Plane Figure for a Cube Materials Needed: 3 Index Cards Scissors Tape Ruler Pencil Directions: 1. Fold two index cards, hamburger style, in half. 2. Tape one edge from each card together. 3. Cut ½ inch off of another index card, hamburger style. 4. Then cut card from part 3 in half to form the top and bottom of the cube. 5. Tape the cards from part 4 as illustrated in the diagram 6. Label the vertices of the cube according to the diagram above. Note: There should be 4 letters on all sides. Tape Edges

18. Questions to Answer 1. How many Planes are in the figure? 2. Write at least 1 name for each of the planes according to the appropriate naming convention. 3. Draw point Z and line m in the plane ABF. 4. What is it called if a point and line are located in the same plane? 5. If two planes intersect (meet), then they intersect in exactly one line. Where does the planes AEB and FGC intersect? Note: Use the proper symbol for naming a line. 6. Does the planes FGC and HEA intersect? Why or why not?