1.1 Points, Lines & Planes +JMJ H. Geo Learning Target: Identify & give examples of undefined terms Euclid: “What’s the point of Geometry? – Euclid” http://www.youtube.com/watch?v =_KUGLOiZyK8&safe=active » When do historians believe that Euclid completed his work? » What key topic did Euclid build on to create all of Geometry? » Why do you think that Euclid’s ideas have lasted for thousands of years? Vocabulary

1. Point: is a location in space. A point has no dimension. It is named by a single captial letter.

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2. Line: consists of an infinite number of points which extend in opposite directions. A line is one-dimensional. A line may be named by using a single lower cse leter OR by any 2 points on the line.

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3. Plane: consits of an infinite number of points which form a flat surface that extends in all directions. A plane is two-dimensional. A plane may be named using a single capital letter OR by using 3 non-collinear points. NOTE: Point, line, and plane are undefined terms. They cannot be defined using other geometric figures

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4. Collinear points: are points that lie on the same line ! Ex:

Honors Geometry Lesson 1

Euclid: “What’s  the  point  of  Geometry?- Euclid” http://www.youtube.com/watch?v=_KUGLOiZyK8&safe=active Æ When do historians believe that Euclid completed his work? Æ What key topic did Euclid build on to create all of Geometry? Æ Why  do  you  think  that  Euclid’s  ideas  have  lasted  for  thousands  of  years?    

Vocabulary 1. A point is a location in space. A point has no dimension. It is named by a single capital

letter. 2. A line consists of an infinite number of points which extend

in opposite directions. A line is one-dimensional. A line may be named by using a single lower case letter OR by any two points on the line.

3. A plane consists of an infinite number of points

which form a flat surface that extends in all directions. A plane is two-dimensional. A plane may be named using a single capital letter OR by using three non-collinear points.

NOTE: Point, line, and plane are undefined terms.

They cannot be defined using other geometric figures. 4. Collinear points are points that lie on the same line. 5. Coplanar points are points that lie on the same plane. 6. A line segment consists of two points on a line (called

the endpoints) and all of the points between them.

Line Segment EF EF

E F

5. Coplanar points: are points that lie on the same plane

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6. Line segment: consits of 2 points on a line (called the endpoints) and all of the points between them.

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7. Ray: consitsts of one point on a line (called the initial point) and all of the points on one side of the intial point

8. Opposite rays: consists of one point on a line ( called the initial point) and all of the points on one side of the initial point.

9. Intersect: is the set of points that the figures have in commone. ! Two or more geometric figures intersect if they have one or more points in

common

10. Postulate (or axiom): is a rule that is accepted without proof

11. Postulate 5: through any 2 points there exists exactly one line

12. Postulate 7: If 2 points lie in a plane, then the line containing them lies in the plane.

13. Postulate 8: Through any 3 noncollinear points there exists exactly one plane

14. Postulate 10: If 2 planes intersect, then their intersection is a line

15. Postulate 11: If 2 lines intersect, then their intersection is exactly one point Notes

11. Draw 3 noncollinear points, A, B, and C. Then draw point D on AB between points A and B. Draw

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CD. Draw CA and CB.

7. A ray consists of one point on a line (called the initial

point) and all of the points on one side of the initial point.

8. Opposite rays share the same initial point and

extend in opposite directions on the same line. 9. Two or more geometric figures intersect if they have one or more points in

common. The intersection is the set of points that the figures have in common.

Think of a rule  in  soccer….we  have  the rules in Geometry, and we call them axioms, or postulates.

10. A Postulate (or axiom) is a rule that is accepted without proof. 11. POSTULATE: Through any two points there exists exactly one line. 12. POSTULATE: If two points lie in a plane, then the line containing them lies in the

plane. 13. POSTULATE: Through any three noncollinear points there exists exactly one

plane. 14. POSTULATE: If two planes intersect, then their intersection is a line. 15. POSTULATE: If two lines intersect, then their intersection is exactly one point.

Activity

Ray EF

EF

E F

AB and AC are opposite rays

A CB

11. Draw three noncollinear points, A, B, and C. Then draw

point D on AB between points A and B. DrawCD. Draw CA andCB. 12. Are points A, B, and D collinear? Are points B, C, and D collinear? 13. Are CA and CBopposite rays? Are DA and DB opposite rays? 14. True or False: ABhas a definite length and thickness. Use the diagram to state the postulate(s) that verifies the truth of the statement. 15. The points X, Y, and Z, lie in a plane (labeled B). 16. The points X and Y lie on a line (labeled m). 17. The planes A and B intersect in a line (labeled l). 18. The points X and Y lie in plane B. Therefore, line m

lies in plane B.

Homework RETURN THE STUDENT INFORMATION SHEET WITH BOTH A STUDENT AND PARENT SIGNATURE Pages 9−11:    13−19,  25−27,  28−29,  31−34  (include  a  sketch  for  each  problem),  39−41,  43,44 And complete the following page:

12. Are points A, B, and D collinear? Are points B, C, and D collinear? 13. Are CA and CB opposite rays? Are DA and DB opposite rays? 14. True or False: AB has a definte length & thickness Use the diagram to state the postulate(s) that verifies the truth of the statement

15. The points X, Y, and Z, lie in a plane (labeled B)

16. The points X and Y lie on a line (labeled m)

17. The planes A and B intersect in a line (labeled l)

18. The points X and Y lie in plane B. Therefore, line m lies in plane B

HW Questions

1. List the 3 undefined terms 2. Define collinear points and coplanr points 3. Explain the differece between a line segment and a line 4. Explain why when 2 planes interesect, they make a line 5. Sketch a picture to help a friend understand the following postulate: If 2 points lie in a

plane, then the line containing them lies in the plane 6. Deomonstrate through a drawing or explain a way to use one of the postulates in the

real world. You may not repeat anything discussed in class today or in this homework =)

11. Draw three noncollinear points, A, B, and C. Then draw

point D on AB between points A and B. DrawCD. Draw CA andCB. 12. Are points A, B, and D collinear? Are points B, C, and D collinear? 13. Are CA and CBopposite rays? Are DA and DB opposite rays? 14. True or False: ABhas a definite length and thickness. Use the diagram to state the postulate(s) that verifies the truth of the statement. 15. The points X, Y, and Z, lie in a plane (labeled B). 16. The points X and Y lie on a line (labeled m). 17. The planes A and B intersect in a line (labeled l). 18. The points X and Y lie in plane B. Therefore, line m

lies in plane B.

Homework RETURN THE STUDENT INFORMATION SHEET WITH BOTH A STUDENT AND PARENT SIGNATURE Pages 9−11:    13−19,  25−27,  28−29,  31−34  (include  a  sketch  for  each  problem),  39−41,  43,44 And complete the following page:

7. There were 5 postulates today. How can you know which postulate to use in what kind of situation? Be specific in identifying the postulate and what to look for in the situation.

8. How do the various definitions that we discussed at the beginning of class compare with each other? What do they have in common? What is different?

9. You are dirving down the road and notice a house. There is a line where the roof of the house and the wall of the house meet. Which postulate is this demonstrating? Explain

10. Jake says that he has 3 points that do not exist in one plane, so therefore the postulate is false. Defend or argue against Jake’s postition. In other words, is he correct and why?