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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