lesson 1.1 points, lines and planes objective: i will be able to… 1.identify and model points,...
TRANSCRIPT
LESS
ON
1-1 Points, Lines, And Planes
1.1 Points, Lines and Planes Objective:I will be able to…1. Identify and model points, lines, and
planes as well as intersecting lines and planes
2. Make generalizations about geometric properties
LESS
ON
1-1 Points, Lines, And Planes
Undefined Terms
Line: made of points that extend in one dimension – no width or depth, but infinite length. 2 points determine a line.A B
AB�������������� �
BA�������������� �
l
line l
Point: a location with no dimensions. Usually represented by a dot and a capital letter. A pt A
LESS
ON
1-1 Points, Lines, And Planes
Plane: made of points that extend infinitely in two directions, but has no height. A flat surface with no thickness. Three noncollinear points determine and name a plane. A capital script letter can also name a plane.
DC
B
A M
LESS
ON
1-1 Points, Lines, And Planes
Defined Term: items defined by means of undefined terms or previously defined terms.
Collinear: points or other objects that all lie on one line.
A BC
DD
LESS
ON
1-1 Points, Lines, And Planes
Defined Term: items defined by means of undefined terms or previously defined terms.
Coplanar: points or other objects that all lie on one plane.
DC
BA M
LESS
ON
1-1 Points, Lines, And Planes
A. Use the figure to name a line containing point K.
Answer: The line can be named as line a.There are three points on the line. Any two of the points can be used to name the line.
EXAMPLE 1
LESS
ON
1-1 Points, Lines, And Planes
B. Use the figure to name a plane containing point L.
You can also use the letters of any three noncollinear points to name the plane.plane JKM plane KLM plane JLM
Answer: The plane can be named as plane B.
There are 15 different three-letter names for this plane (any order)
EXAMPLE 1
LESS
ON
1-1 Points, Lines, And Planes
A. Use the figure to name a line containing the point X.
Line c
EXAMPLE 1
B. Use the figure to name a plane containing point Z.
Plane P
LESS
ON
1-1 Points, Lines, And Planes
A. Name the geometric shape modeled by a 10 12 patio.
Answer: The patio models a plane.
Real World EXAMPLE 2
LESS
ON
1-1 Points, Lines, And Planes
LESS
ON
1-1 Points, Lines, And Planes
Point
A. Name the geometric shape modeled by a colored dot on a map used to mark the location of a city.
Real World EXAMPLE 2
LESS
ON
1-1 Points, Lines, And Planes
Plane
B. Name the geometric shape modeled by the ceiling of your classroom.
Real World EXAMPLE 2
LESS
ON
1-1 Points, Lines, And Planes1. Name a line that contains point A.
Try 2-5 on your own…
2. What is another name for line ℓ? 3. Name a point not on .
LESS
ON
1-1 Points, Lines, And Planes
Draw a surface to represent plane R and label it.
EXAMPLE 3
LESS
ON
1-1 Points, Lines, And Planes
Draw a line anywhere on the plane.
EXAMPLE 3
LESS
ON
1-1 Points, Lines, And Planes
Draw dots on the line for point A and B. Label the points.
EXAMPLE 3
LESS
ON
1-1 Points, Lines, And PlanesEXAMPLE 3
LESS
ON
1-1 Points, Lines, And Planes
Draw dots on this line for point D and E. Label the points.
EXAMPLE 3
LESS
ON
1-1 Points, Lines, And Planes
Label the intersection point of the two lines as P.
EXAMPLE 3
LESS
ON
1-1 Points, Lines, And Planes
Answer:
EXAMPLE 3
LESS
ON
1-1 Points, Lines, And Planes
A. B.
C. D.
A. Choose the best diagram for the given relationship. Plane D contains line a, line m, and line t, with all three lines intersecting at point Z. Also, point F is on plane D and is not collinear with any of the three given lines.
EXAMPLE 3
LESS
ON
1-1 Points, Lines, And Planes
A. How many planes appear in this figure?
Answer: There are two planes: plane S and plane ABC.
EXAMPLE 4
LESS
ON
1-1 Points, Lines, And Planes
B. Name three points that are collinear.
Answer: Points A, B, and D are collinear.
EXAMPLE 4
LESS
ON
1-1 Points, Lines, And PlanesTry on your own!Refer to the figure.How many planes are shown in the figure?
How many of the planes contain points F and E?
Name four points that are coplanar.
Are points A, B, and C coplanar? Explain.
LESS
ON
1-1 Points, Lines, And Planes
1. Name the intersection of plane N and line .
2. Name the intersection of and .
3. Does intersect ? Explain.
LESS
ON
1-1 Points, Lines, And Planes
WT�������������� �
What is this?
Example 6
LESS
ON
1-1 Points, Lines, And Planes
W
What is this?
Example 6
LESS
ON
1-1 Points, Lines, And Planes
What is this?
Example 6
ABC
LESS
ON
1-1 Points, Lines, And PlanesUndefined term: a term that is only explained using examples and descriptions
Point: a location with no dimensions; it has no shape or size
Line: made up of points and has no thickness or width (1 dimension); must have 2 points for a line
Plane: a flat surface made up of points that extends infinitely in all directions (2 dimensions); must have 3 non-collinear points for a plane
LESS
ON
1-1 Points, Lines, And PlanesCollinear: points that lie on the same line
Coplanar: points that lie on the same plane
Intersection: the set of points they have in common What do 2 intersecting lines have in common? What do 2 intersecting planes have in common? What do an intersecting line and a plane have in common?
Defined term: explained using undefined terms and/or other defined terms