Points Lines and Planes. Unit 1 Lesson 2
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1 Unit 1 Lesson 2
2 Students will be able to: Draw points, lines, line segments, rays, and planes. Identify points, lines, line segments, rays and planes. Know precise definitions of line, and line segment, based on the undefined notions of point, line.
3 Key Vocabulary: A line, A point, A line segment, A plane, Intersection.
4 In geometry, some words, such as point, line, and plane, are undefined terms. Although these words are not formally defined, it is important to have general agreement about what each word means. A point has no dimension. It is usually represented by a small dot and named by a capital letter.
5 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, and is named by two points on the line or a lowercase script letter.
6 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, and is named by a capital script letter or 3 noncollinear points.
7 A line segment is a set of points and has a specific length i.e. it does not extend indefinitely. It has no thickness or width, is usually represented by a straight line with no arrowheads to indicate that it has a fixed length, and is named by two points on the line segment with a line segment symbol above the letters.
8 A ray is a set of points and extends in one dimension in one direction (not in two directions). It has no thickness or width, is usually represented by a straight line with one arrowhead to indicate that it extends without end in the direction of the arrowhead, and is named by two points on the ray with a ray symbol above the letters
9 Collinear points are points that lie on the same line. Coplanar points are points that lie on the same plane.
10 Sample Problem 1: Use the figure to name each of the following. a. A D C Line Points Collinear points Non collinear points
11 Sample Problem 1: Use the figure to name each of the following. a. A D C Line A Points A,, C and D Collinear points A, Non collinear points A, C, D
12 Sample Problem 1: Use the figure to name each of the following. b. K Line segment Points L
13 Sample Problem 1: Use the figure to name each of the following. b. K Line segment KL Points K, L L
14 Sample Problem 1: Use the figure to name each of the following. c. S R O T I Plane Ray Points Coplanar points Non coplanar points
15 Sample Problem 1: Use the figure to name each of the following. c. S R O T I Plane STO Ray IR Points S, T, O, R and I Coplanar points S, T, O Non coplanar points R, I
16 Two or more geometric figures intersect, if they have one or more points in common. The intersection of the figures is the set of points the figures have in common.
17 Postulate 1-1 Through any two points there is exactly one line. Postulate 1-2 If two distinct lines intersect, then they intersect in exactly one point. Postulate 1-3 If two distinct planes intersect, then they intersect in exactly one line. Postulate 1-4 Through any three non collinear points there is exactly one plane.
18 Sample Problem 2: Refer to each figure. a. D Q S W T U Z Name the intersection of line QZ and segment WU.
19 Sample Problem 2: Refer to each figure. a. D Q S W T U Z Name the intersection of line QZ and segment WU. Point T
20 Sample Problem 2: Refer to each figure. a. D Q S W T U Z Name the intersection of plane and line D.
21 Sample Problem 2: Refer to each figure. a. D Q S W T U Z Name the intersection of plane and line D. Point S
22 Sample Problem 2: Refer to each figure. a. D Q S W T U Z Name the two opposite rays at point T.
23 Sample Problem 2: Refer to each figure. a. D Q S W T U Z Name the two opposite rays at point T. TQ and TZ
24 Sample Problem 2: Refer to each figure. a. D Q S W T U Z What is another name for plane?
25 Sample Problem 2: Refer to each figure. a. D Q S W T U Z What is another name for plane? Plane TSU
26 Sample Problem 2: Refer to each figure. b. L M C S G Name the intersection of plane and plane τ. T τ
27 Sample Problem 2: Refer to each figure. b. L M C S G Name the intersection of plane and plane τ. Line S τ T
28 Sample Problem 2: Refer to each figure. b. L M C S G What is another name for plane? T τ
29 Sample Problem 2: Refer to each figure. b. L M C S G What is another name for plane? Plane LMG T τ
30 Sample Problem 2: Refer to each figure. b. L M C S G Name the intersection of line MG and line S. T τ
31 Sample Problem 2: Refer to each figure. b. L M C S G Name the intersection of line MG and line S. Point C τ T
32 Sample Problem 2: Refer to each figure. b. L M C S G Name a point that is collinear with M and C. Point G τ T
33 Sample Problem 2: Refer to each figure. c. τ H L P Name the intersection of plane and line LC. C J
34 Sample Problem 2: Refer to each figure. c. τ H L C J P Name the intersection of plane and line LC. Point C
35 Sample Problem 2: Refer to each figure. c. τ H L P Name the intersection of plane τ and line LC. C J
36 Sample Problem 2: Refer to each figure. c. τ H L C J P Name the intersection of plane τ and line LC. Point L
37 Sample Problem 2: Refer to each figure. c. τ H L P Name a point that is coplanar with H and L. C J
38 Sample Problem 2: Refer to each figure. c. τ H L C J P Name a point that is coplanar with H and L. Point P
39 Sample Problem 2: Refer to each figure. c. τ H L P Name the opposite ray of ray C. C J
40 Sample Problem 2: Refer to each figure. c. τ H L P Name the opposite ray of ray C. C J Ray CJ
41 Sample Problem 3: Draw and label figure for each relationship. a. Plane AS contains lines A, CD, and AK. Lines A and CD intersect in point G. Lines CDand AK intersect in point S. Lines A and AK intersect in point A.
42 Sample Problem 3: Draw and label figure for each relationship. a. Plane AS contains lines A, CD, and AK. Lines A and CD intersect in point G. Lines CDand AK intersect in point S. Lines A and AK intersect in point A. A C G S D K
43 Sample Problem 3: Draw and label figure for each relationship. b. Plane contains line A and point L. Plane τ contains line EF and point S. Lines A and EF intersect in point H. The intersection of plane and plane τ is line LU.
44 Sample Problem 3: Draw and label figure for each relationship. b. Plane contains line A and point L. Plane τ contains line EF and point S. Lines A and EF intersect in point H. The intersection of plane and plane τ is line LU. A L τ E H F S U
45 Sample Problem 3: Draw and label figure for each relationship. c. Plane and plane τ do not has intersect. Plane ε intersect plane in line C. Plane ε intersect plane τ in line ER.
46 Sample Problem 3: Draw and label figure for each relationship. c. Plane and plane τ do not has intersect. Plane ε intersect plane in line C. Plane ε intersect plane τ in line ER. C E τ R ε
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