Section 1.1 Points, Lines, and Planes

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Section 1.1 Points, Lines, and Planes
­
All geometric shapes are made of points. ­
In Geometry you will learn about those shapes and their characteristics.
­ A point is simply a location.
­
A line is made up of points and has no thickness or width. A
B
n
­ Points on the same line are said to be collinear.
­
A plane is a flat surface made up of points. X
Y
Z
T
­ Points that lie on the same plane are said to be coplanar.
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­ A plane has no depth and extends infinitely in all directions.
­ Points are often used to name lines and planes.
­ The letters of the points can be in any order.
2
Ex 1 Use the figure to name each of the following:
a. a line containing point A
b. a plane containing point C
Ex 2 Name the geometric shapes modeled by the picture.
3
Ex 3 Name the geometric shape modeled by each object.
a. the long hand on a clock
b. a 10 x 12 patio
c. the location where the corner of a driveway meets the road
­ In geometry, point, line, and plane are considered undefined terms because they are only explained using examples and descriptions. 4
Ex 4 Draw and label a figure for each relationship.
a. Lines GH and JK intersect at L for , , and K(2,­3) on a coordinate plane. Point M is coplanar with these points, but not collinear with GH and JK.
b. TU lies in plane Q and contains point R.
c. plane R contains lines AB and DE, which intersect at point P. Add point C on plane R so that it is not collinear with AB or DE.
d. QR on a coordinate plane contains P(4,­4) and Q (­2,4). Add point T so that T is collinear with these points.
5
­
Space is a boundless, three­dimensional set of all points. ­
Space contains lines and planes.
Ex 5 a. How many planes appear in this figure?
b. Name three points that are collinear.
c. Are points G, A, B, and E coplanar? Explain.
d. At what point do EF and AB intersect? 6
Modeling Intersecting Planes Activity
1. Draw a line where the two planes meet. The intersection of two planes is a line, so let’s label two points on the line, C and D.
2. Draw a point F on your model so that it lies in Q but not in R. Can F lie on DC?
3. Draw point G so that it lies in R, but not in Q. Can G lie on DC?
4. If point H lies in both Q and R, where would it lie? Draw point H on your model.
5. Draw a sketch of your model on paper. Label all points, lines, and planes appropriately.
Assign Pgs. 9 ­ 11 # 4 ­ 10, 12 ­ 18, 21 ­ 27, 30 ­ 35, 37, 41, 43
Pg. 12 Read page and do # 1, 2
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Example 1 Draw 3 planes that do not intersect.
Example 2 Draw plane W. Line BC lies in plane W, line AD intersects plane W at point E.
Example 3 Lines a, b, and c are coplanar, but do not intersect.
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