1. Welcome to Geometry
Ms. Urquhart

2. Identify Points, Lines, and Planes
Lesson 1-1
Identify Points, Lines, and Planes
Lesson 1-1 Point, Line, Plane

3. Points (Undefined term)
Points do not have actual size.
How to Sketch:
Using dots
How to label:
Use capital letters
Never name two points with the same letter
(in the same sketch). A B C A
Lesson 1-1 Point, Line, Plane

4. Lines (Undefined Term)
Lines extend indefinitely and have no thickness or width.
How to sketch : using arrows at both ends.
How to name: 2 ways
(1) small script letter – line n
(2) any two points on the line -
Never name a line using three points - n A B C
Lesson 1-1 Point, Line, Plane

5. Lesson 1-1 Point, Line, Plane
Collinear Points
Collinear points are points that lie on the same line. (The line does not have to be visible.)
A point lies on the line if the coordinates of the point satisfy the equation of the line.
Ex: To find if A (1, 0) is collinear with
the points on the line y = -3x + 3.
Substitute x = 1 and y = 0 in the equation.
0 = -3 (1) + 3
0 =
0 = 0
The point A satisfies the equation, therefore the point is collinear
with the points on the line. A B C
Collinear C A B
Non collinear
Lesson 1-1 Point, Line, Plane

6. Planes are 2 dimensional
A plane is a flat surface that extends indefinitely in all directions.
How to sketch: Use a parallelogram (four sided figure)
How to name: 2 ways
(1) Capital letter without a dot – Plane M
(2) Any 3 non-collinear points in the plane - Plane: ABC/ ACB / BAC / BCA / CAB / CBA
Link to movie on green plane A M B C
Horizontal Plane
Vertical Plane
Other
Lesson 1-1 Point, Line, Plane

7. Different planes in a figure:B
Plane ABD
Plane FGH
Plane BCF
Plane DHE
Plane BEF
Plane CDG
Etc. D C E F H G
Lesson 1-1 Point, Line, Plane

8. Other planes in the same figure:
Any three non collinear points determine a plane!
Plane FGD
Plane ACE
Plane ACH
Plane AGF
Plane BDG
Etc.
Lesson 1-1 Point, Line, Plane

9. Lesson 1-1 Point, Line, Plane
Coplanar Objects
**Remember: Any 3 non-collinear points determine a plane!
Coplanar objects (points, lines, etc.) are objects that lie on the same plane. The plane does not have to be visible.
Are the following points coplanar?
A, B, C ?
Yes
A, B, C, F ? No
H, G, F, E ?
Yes
E, H, C, B ?
Yes
A, G, F ?
Yes
C, B, F, H ? No
Lesson 1-1 Point, Line, Plane

10. Lesson 1-1 Point, Line, Plane
Example 1
a. Give two other names for
b. Give two other names for plane R
c. Name three points that are collinear
d. Name four points that are coplanar.
Line n and QP
plane VSP, plane SVT, plane PVT, etc.
points S,P, and T
Points T,V,S, and P or points S,P, T, and Q
Lesson 1-1 Point, Line, Plane

11. Lesson 1-1 Point, Line, Plane
Segment
a straight line which links 2 points without extending beyond them.
The symbol for line segment AB is
Lesson 1-1 Point, Line, Plane

12. Lesson 1-1 Point, Line, Plane
Rays B A
have a beginning point but no end point.  Think of sun's rays: they start at sun and go on forever...
Opposite Rays: 2 rays that lie on the same line, with a common endpoint and no other points in common. 
How to Name? AB
Opposite rays form a straight line and/or a straight angle (180°).
AB and AC are opposite rays
*When labeling: we always start with the endpoint first and the arrow points to the right.
Lesson 1-1 Point, Line, Plane

13. Lesson 1-1 Point, Line, Plane
EXAMPLE 2
a. Give another name for .
b. Name all rays with endpoint J.
Which of these rays are opposite rays?
Lesson 1-1 Point, Line, Plane

14. Intersection of Figures
The intersection of two figures is the set of points that are common in both figures.
The intersection of two lines is a point. m
Line m and line n intersect at point P. P n
Continued…….
Lesson 1-1 Point, Line, Plane

15. 3 Possibilities of Intersection of a Line and a Plane
(1) Line passes through plane – intersection is a point.
(2) Line lies on the plane - intersection is a line.
(3) Line is parallel to the plane - no common points.
Lesson 1-1 Point, Line, Plane

16. Intersection of Two Planes is a Line.B P A R
Plane R and Plane P intersect at the line
Lesson 1-1 Point, Line, Plane

17. Lesson 1-1 Point, Line, Plane
GUIDED PRACTICE
Use the diagram at the right.
5. Name the intersection of and line k.
6. Name the intersection of plane A and plane B.
7. Name the intersection of line k and plane A.
Point M
line k
line k
Lesson 1-1 Point, Line, Plane