1.1 Points, Lines, and Planes
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1 1.1 Points, Lines, and Planes Identify and model points, lines and planes. Identify collinear, and coplanar points and intersecting lines and planes in the space. Vocabulary Point, line, plane, collinear, coplanar, space, segment, ray, opposite ray, midpoint, congruent, bisects.
2 Prerequisite skills. Graph and label each point in the coordinate plane. A(3, -2) B(4, 0) C(-4, - 4) D( -1, 2 ) D(-1,2) B(4,0) A(3, - 2) C(-4,- 4)
3 Undefined terms The terms point, line, and plane can be explained using examples and descriptions.
4 Point 3 Undefined Terms of Geometry Is a location. No dimensions. Represented by a small dot and by a capital letter. A B
5 3 Undefined Terms Continues line -A line is a series of points that extend in two opposite directions w/o end. -Defined by any two points on the line. -Name a line by two capital letters or a lower case letter Points on the same line are said to be Collinear. A B C n AC AB BC line n Noncollinear means not lying on the same line.
6 The last of the Undefined Terms Plane A flat surface that extends indefinitely Contains lines and points Named by 3 Noncollinear points or by a capital script letter. Points & lines in the same plane are coplanar. Notation: XZY or Plane plane XYZ n plane ZYX t z x y t Geogebra Through any three noncollinear points there is exactly one plane.
7 Segment A segment is part of a line that consists of two points, called endpoints, and all points between them. Segment symbol A B AB BA Length of a segment AB OR mab
8 Two segments are congruent if and only if they have equal measures, or lengths. C 3.2 cm 3.2 cm A D Use is equal to With numbers. AC=DC 3.2 cm=3.2 cm Use is congruent to with figures. AC DC
9 When drawing figures, show congruent segments by making identical marking. C A D
10 Midpoint The midpoint of a segment is the point on the segment that is the same distance (equidistant) from both end points. The midpoint bisects the segment, or divide the segment into two congruent segments. J C E 2 cm F CF FD CF FD G 2 cm D H L K JK KL HJ HL M N P
11 The Midpoint Formula The coordinates of the midpoint of a line segment are the average of the coordinates of its endpoints. The Midpoint Formula : x 1 x2 y1 y2 2, 2
12 Midpoint Number Line Coordinate Plane
13 Midpoint Number Line
14 Midpoint Coordinate Plane (1, 4.5) x x y y 1 2, , (1, 4.5)
15 Ray A Ray is part of the line that consists of one end point an all the points of the line on one side of the end point A B AB A B BA AB and BA are opposite rays
16 Intersection The point or set of points common to two geometric figures A k r
17 Intersection q E D A B C p If two planes intersect, then they intersect in exactly one line.
18 Intersection B w A D E F f m C p
19 Space Space is a boundless, three dimensional set of all points. Space can contain lines and planes F D G E A H B C
20 F D G E A H B C How many planes appears in this figure? Name three points that are collinear. Are points G,B,C and E coplanar? Explain At what point do EF and AB intersect?
21 Through any three noncollinear points there is exactly one plane. C A H D B E Which plane contains the points: A, B, C Which plane contains the points: F, B, E Which plane contains the points: A, B, F G F
22 Example 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.
23 Example Use the figure to name a plane containing point L. Answer: The plane can be named as plane B. You can also use the letters of any three noncollinear points to name the plane. plane JKM plane KLM plane JLM
24 Draw and label a figure for the following situation. Plane R contains lines and, which intersect at point P. Add point C on plane R so that it is not collinear with or. Draw a surface to represent plane R and label it.
25 Draw and label a figure for the following situation. Plane R contains lines and, which intersect at point P. Add point C on plane R so that it is not collinear with or. Draw a line anywhere on the plane.
26 Draw and label a figure for the following situation. Plane R contains lines and, which intersect at point P. Add point C on plane R so that it is not collinear with or. A B Draw dots on the line for points A and B. Label the points.
27 Draw and label a figure for the following situation. Plane R contains lines and, which intersect at point P. Add point C on plane R so that it is not collinear with or. A B Draw a line intersecting.
28 Draw and label a figure for the following situation. Plane R contains lines and, which intersect at point P. Add point C on plane R so that it is not collinear with or. A E D B Draw dots on this line for points D and E. Label the points.
29 Draw and label a figure for the following situation. Plane R contains lines and, which intersect at point P. Add point C on plane R so that it is not collinear with or. A E D P B Label the intersection point of the two lines as P.
30 Draw and label a figure for the following situation. Plane R contains lines and, which intersect at point P. Add point C on plane R so that it is not collinear with or Answer: A E C D P B Draw a dot for point C in plane R such that it will not lie on or. Label the point.
31 Segment: The portion of the line between two points. Find the length of Answer: 18 mm
32 Find the length of. Each inch is divided into sixteenths. Point E is closer to the 3-inch mark. Answer: is about 3 inches long.
33 Segment Addition Postulate Find LM. Point M is between L and N. Sum of parts whole LM + MN = LN
34 Homework Workbook 1.1
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