Trigonometry
Geometry Lesson Notes 1.1A Date ________________
Objective: Identify and model points, lines, and planes. Identify collinear points and
intersecting lines in a plane.
Point: (a location)
We imagine a dot, but in geometry, a point has no dimension, no size.
Named by a capital letter.
Identified on the coordinate plane by an ordered pair.
Line: (a straight segment connecting 2 points and then extending infinitely in both directions)
It takes 2 points to define a line.
There is exactly one line through any 2 points.
Lines have no thickness. A line contains an infinite number of points.
Named by a lowercase script letter or by 2 points on the line with a double arrow above.
or or _____________________
Collinear: points are collinear if they are on the same line.
Noncollinear: points are noncollinear if they are not on the same line.
Plane: (a flat surface made up of points)
We visualize a 2-dimensional region, but a plane has no thickness and
extends indefinitely.
It takes 3 noncollinear points to define a plane.
There is exactly one plane through any
three noncollinear points.
Named by a capital script letter or by 3 noncollinear points.
Coplanar: points are coplanar if they are on the same plane.
NOTE: Point, Line, and Plane are not actually defined. They are “undefined terms” because
they are only explained using examples and descriptions.
Practice:
Figures intersect at the points that are in both figures.
2 lines intersect at a _______________ .
2 planes intersect at a _______________ .
Think about it: How can a plane and a line intersect?
How can 2 or more lines not intersect?
How can 2or more planes not intersect?
How can a line and a plane not intersect?
Draw intersecting planes.
Example 2 (p 7): Model Points, Lines, and Planes
How can a sheet of lined paper be used to model point, line, and plane?
Name other examples of things that model a point, a line, and a plane.
Example 1 (p 7): Name Lines and Planes
a. Name a line containing point L.
b. Name a plane containing point M.
c. Draw [pic], a line in B intersecting
[pic] at N.
c. Draw a line intersecting B at J.
Example 3 (p 7): Draw Geometric Figures
For a-c:
Given G(−5, −6), H(4, 8), J(−7, 2),
and K(3, −4)
a. Draw [pic] and [pic] intersecting at L.
b. Draw M noncollinear with [pic]and [pic].
c. Draw T collinear with [pic].
d. Draw a plane R that contains [pic] and [pic] which intersect at point P.
Add point C on plane R so that it is not collinear with [pic] or [pic].
( HW: A2 pp 9-10 #13-20, 22-26 even, 29
Geometry Lesson Notes 1.1B Date ________________
Objective: Identify collinear and coplanar points and intersecting lines and planes in space.
Space: (a boundless, 3-dimensional set of all points)
Space contains lines and planes.
Example 4 (p 8): Interpret Drawings
Figure 1:
a. How many planes in the figure?
b. Name 3 collinear points.
c. Are B, C, D, and E coplanar?
d. Where does [pic] intersect B ?
e. Where does [pic] intersect [pic]?
f. Name a plane containing [pic] and H.
Figure 2:
a. How many planes appear in the
figure?
b. Name three collinear points.
c. Are points A, B, C, and D coplanar?
Explain.
d. Are points A, B, C, and E coplanar?
Explain.
e. At what point do [pic] and [pic] intersect?
( HW: A3 pp 10-11 #30-45
( HW: A2-3 pp 9-11 #13-20, 22-26 even, 29-45 odd
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