Section 1.2Points, Lines & Planes: Section 1.2 Points, Lines & Planes Geometry Mrs. Adams
Notetaking Guide pp. 4-6
Slide2: Undefined Terms in Definitions A definition uses known words to describe a new word.
In geometry, some words such as point, line and plane are undefined terms or not formally defined.
Slide3: Vocabulary Point A point has no dimension.
It is usually represented by a small dot. A Point A Vocabulary
Slide4: A line extends in one dimension.
It is usually represented by a straight line with two arrowheads to indicate that the line extends without end in two directions. A B l Vocabulary Line Line l or
Slide5: Vocabulary Plane A plane extends in two dimensions.
It is usually represented by a shape that looks like a tabletop or wall.
You must imagine that the plane extends without end even though the drawing of a plane appears to have edges.
A M Plane M or plane ABC B C
Slide6: A Few More Things… A point lies on a line or on a plane.
Collinear points: points that lie on the same line Coplanar points: points that lie on the same plane
Slide7: a. Name 3 points that are collinear. Solution Points ___, ___, and ___ lie on the same line, so they are collinear. D A C D A B C E Example 1 ~ Naming Points
Slide8: Name 3 points
that are coplanar. Solution There are many correct answers. For instance, points ___, ___, and ___ lie on the same plane.
Also points ___, ___, and ___ are coplanar, although the plane containing them is not drawn. D D A B C E A B B E A Example 1 ~ Naming Points
Slide9: Example 1 ~ Naming Points c. Name 4 points
that are not coplanar. Solution There are many correct answers. For instance, points ___, ___, ___, and ___ do not lie on the same plane. C D A B C E A B E
Slide10: Checkpoint 1. Name 3 points that are not collinear. Solution E E, F, G H G F A B C D
Slide11: Vocabulary A line segment is part of a line that consists of 2 points, called endpoints, and all points on the line between the endpoints.
A B A B M
Slide12: Vocabulary A B A ray is part of a line that consists of a point, called an initial point, and all points on the line that extend in one direction. not
Slide13: Just a little side note… A B Note that is the same as and
is the same as .
However, and are not the same.
They have different initial points
and extend in different directions.
Slide14: If C is between A and B on ,
then and are opposite rays. A B Vocabulary C
Slide15: Example 2 ~ Drawing Lines, Segments, and Rays A, B, C and D are shown.
Draw .
Draw .
Draw .
Draw .
Draw .
B A C D
Slide16: Example 3 ~ Drawing Opposite Rays X Z Draw a line. Label 3 points on the line and name a pair of opposite rays. Draw points X, Y, and Z on the given line so that Y is between X and Z. The opposite rays are
____ and ____. Y
Slide17: Two or more geometric figures intersect if they have one or more points in common. Vocabulary The intersection of the figures is the set of points that the figures have in common.
Slide18: Try This… Turn to page 12 in your textbook. Label the index cards and cut the slots as shown. 1. What is the intersection of and ? of and ? G G Slide the cards together. What is the intersection of and ? G What is the intersection of planes M and N?
Slide19: Example 4 ~ Sketching Intersection Sketch two lines that do not intersect and a line that intersects each of the other lines. Draw a line that does not intersect the given line. Then draw a third line that intersects the first two lines. Emphasize the points of intersection.
Slide20: Example 5 ~ Sketching Intersection A line that intersects a plane in one point. Sketch the figure described. Draw a plane and a line.
Emphasize the point
where they meet.
Dashes indicate where the
line is hidden by the plane.
Slide21: Example 6 ~ Sketching Intersection Two planes that intersect in a line. Sketch the figure described. Draw two planes.
Emphasize the line
where they meet.
Dashes indicate where one
plane is hidden by the
other plane.
Slide22: Checkpoint Draw points A, B, and C so that they are not
collinear. Then sketch and . Sketch the figure described. A B C
Slide23: Checkpoint 4. Sketch two planes that do not intersect and a line that intersects each plane in a point. Sketch the figure described.
ASSIGNMENT: ASSIGNMENT Text p. 13
(1-35 all, 33-66 even)