Terms, notation, and representation Student Activity Sheet 1; use with Overview

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1 Student: Class: Date: Student Activity Sheet 1; use with Overview 1. REEVVI IEEW Graph the following points on the coordinate plane. A (1,4) B (-5,0) C (0,8) D (3,-5) E (0,-2) F (-8,-4) G (4,0) H (-7,7) 2. In the picture below, find as many geometric objects as you can. Activity sheet 1, Page 1 of 1

2 Student: Class: Date: 1. What are the three undefined terms in geometry? 2. Write a description of a point. How are points labeled? 3. Write a description of a line. How are lines labeled? 4. What are two names for the line containing points A and E? Activity sheet 2, Page 1 of 7

3 Student: Class: Date: 5. Describe the difference between a line and a line segment. 6. What is meant by the notations AE, AE, and AE? 7. Write a definition of ray. 8. How do you name a ray in geometry? What is the name of a ray with endpoint I and point J on the ray? Activity sheet 2, Page 2 of 7

4 Student: Class: Date: 9. Using the notations provided, complete the table by writing in the correct notation for each name and figure. AB BA AB BA AB BA AB BA 10. REEI INFFORRCCEE Draw and label LM where L has coordinates (3,-2) and M has coordinates (-1,5) Activity sheet 2, Page 3 of 7

5 Student: Class: Date: 11. Write a definition of angle. 12. In this picture, one angle shown is!dbg. Write four ways to name the other angle. 13. What is the difference between!dbg and m!dbg? Activity sheet 2, Page 4 of 7

6 Student: Class: Date: 14. Using the angle names provided, label the angles in the diagram below.!b!eaf!a!ecd!fea!1!cba!dca 15. REEI INFFORRCCEE Suppose A and B are complementary angles, m A = (3x + 5), and m B = (2x 15). Solve for x and then find m A and m B. 16. REEI INFFORRCCEE The measure of the supplement of an angle is 12 more than twice the measure of the angle. Find the measures of the angle and its supplement. Activity sheet 2, Page 5 of 7

7 Student: Class: Date: 17. Write a description of a plane in geometry. 18. What is the minimum number of points needed to determine a line? A plane? Activity sheet 2, Page 6 of 7

8 Student: Class: Date: 19. Name two points in the illustration that are collinear with points C and F. 20. Points H, K, and J are noncollinear points. Name another point that is noncollinear with points H and K. 21. Points C, Q, and S are coplanar points. Name another point on the floor that is coplanar with C and Q. 22. Points A, B, C, and F are noncoplanar points. Name another point in the room that is noncoplanar with A, B, and F. Activity sheet 2, Page 7 of 7

9 Student: Class: Date: Student Activity Sheet 3; use with Exploring Investigating points, lines and planes 1. What parts of the box represent points? 2. What parts of the box represent lines? 3. What parts of the box represent planes? 4. What does the box itself represent? 5. What geometric object best represents the intersection of two lines? Activity sheet 3, Page 1 of 3

10 Student: Class: Date: Student Activity Sheet 3; use with Exploring Investigating points, lines and planes 6. How many lines intersect at each vertex of the box? 7. What geometric figure represents the intersection of two planes? 8. How many lines exist through any two points? 9. Consider corners B, D, and F on the box, and answer the following questions. a. What plane or planes contain all three corners? b. How many planes contain these three points? c. What is another name for this plane? 10. Complete the following sentence. Through any three noncollinear points there exists. 11. How many planes pass through three collinear points? Activity sheet 3, Page 2 of 3

11 Student: Class: Date: Student Activity Sheet 3; use with Exploring Investigating points, lines and planes Using the terms provided, complete the following sentences. In sentences 14-16, assume that the two lines or planes are distinct and that they intersect. planes lines point plane collinear points two line three one noncollinear 12. A line is determined by exactly. 13. A plane is determined by exactly. 14. Two lines intersect in exactly. 15. Two planes intersect in exactly. 16. Two intersecting lines lie in exactly. Activity sheet 3, Page 3 of 3

12 Student: Class: Date: Student Activity Sheet 4; use with Exploring Moving into hyperspace 1. Name a geometric object that represents each of the following dimensions. a. Zero dimension: b. One dimension: c. Two dimensions: d. Three dimensions: 2. Since the face of a 3-D cube is a 2-D square, what shape is the face of a hypercube, or 4-D cube? 3. REEI INFFORRCCEE Complete the following table. You do not need to fill in any of the blank cells of the table that are shaded. Dimensions Object Number of vertices Number of lines Number of planes 0 point 1 1 line 2 square 3 cube 4 hypercube Consider what a 5-dimensional object consists of! Activity sheet 4, Page 1 of 1

13 Teacher Version Student Activity Sheet 1; use with Overview 1. REEVVI IEEW Graph the following points on the coordinate plane. A (1,4) B (-5,0) C (0,8) D (3,-5) E (0,-2) F (-8,-4) G (4,0) H (-7,7) 2. In the picture below, find as many geometric objects as you can. [OV, screen 1] Sample answers: Points Line segments Angles Polygons Rectangular prisms Activity sheet 1, Page 1 of 1

14 Teacher Version 1. What are the three undefined terms in geometry? [EX1, screen 1] Point, line, and plane 2. Write a description of a point. How are points labeled? [EX1, screen 2] A point describes a location but has no size. Geometric figures are made up of sets of points. Points are labeled with capital print letters. 3. Write a description of a line. How are lines labeled? [EX1, screen 3] A straight line or line is made up of an infinite number of points and extends infinitely far in opposite directions. A line has no thickness and no finite length. A line is named using any two points on the line or by labeling it with a lower case letter. When a line is named using two points on the line, a double arrow bar is drawn above the letters. 4. What are two names for the line containing points A and E? [EX1, screen 3] The line can be named AE or EA. Activity sheet 2, Page 1 of 7

15 Teacher Version 5. Describe the difference between a line and a line segment. [EX1, screen 4] A line continues indefinitely in opposite directions, while a line segment is a portion of a line between two points on the line. 6. What is meant by the notations AE, AE, and AE? [EX1, screen 4] AE means the distance between points A and E. AE means the line segment from A to E. AE means the line going through points A and E. 7. Write a definition of ray. [EX1, screen 5] A ray is a subset of a line. A ray starts at one point on a line and extends indefinitely along the line in one direction. 8. How do you name a ray in geometry? What is the name of a ray with endpoint I and point J on the ray? [EX1, screen 5] To name a ray in geometry, use the endpoint of the ray and one other point on the ray. When naming a ray, the order of the points is important. The endpoint of the ray always comes first. For example, IJ describes a ray with endpoint I and point J on the ray. Activity sheet 2, Page 2 of 7

16 Teacher Version 9. Using the notations provided, complete the table by writing in the correct notation for each name and figure. [EX1, screen 6] AB BA AB BA AB BA AB BA 10. REEI INFFORRCCEE Draw and label LM where L has coordinates (3,-2) and M has coordinates (-1,5). 8 M L -4 Activity sheet 2, Page 3 of 7

17 Teacher Version 11. Write a definition of angle. [EX1, screen 7] An angle is the union of two rays that have the same endpoint. The common endpoint is called the vertex of the angle. The rays forming the angle are called the sides of the angle. 12. In this picture, one angle shown is!dbg. Write four ways to name the other angle. [EX1, screen 7]!1,!A,!EAF, or!fae 13. What is the difference between!dbg and m!dbg? [EX1, screen 8] The first names a set of points and the second names a number, specifically the measurement of the angle (usually in degrees). Activity sheet 2, Page 4 of 7

18 Teacher Version 14. Using the angle names provided, label the angles in the diagram below. [EX1, screen 9]!B!EAF!A!ECD!FEA!1!CBA!DCA 15. REEI INFFORRCCEE Suppose A and B are complementary angles, m A = (3x + 5), and m B = (2x 15). Solve for x and then find m A and m B. (3x + 5) + (2x 15) = 90 5x 10 = 90 5x = 100 x = 20 m A = (3(20) + 5) = 65 m B = (2(20) 15) = REEI INFFORRCCEE The measure of the supplement of an angle is 12 more than twice the measure of the angle. Find the measures of the angle and its supplement. Let x = the angle measure. Then 180 x is the measure of the supplement. 180 x = x 168 = 3x x = x = 124 The measures of the angle and its supplement are 56 and 124. Activity sheet 2, Page 5 of 7

19 Teacher Version 17. Write a description of a plane in geometry. [EX1, screen 11] A plane is a flat surface that extends in all directions. 18. What is the minimum number of points needed to determine a line? A plane? [EX1, screen 12] While two points determine a line, it takes three points that do not lie on the same line to determine a plane. Activity sheet 2, Page 6 of 7

Teacher Version 19. Name two points in the illustration that are collinear with points C and F. [EX1, screen 13] Points Q and R are collinear with C and F. 20.

20 Teacher Version 19. Name two points in the illustration that are collinear with points C and F. [EX1, screen 13] Points Q and R are collinear with C and F. 20. Points H, K, and J are noncollinear points. Name another point that is noncollinear with points H and K. [EX1, screen 13] Any other point in the diagram is noncollinear with H and K. 21. Points C, Q, and S are coplanar points. Name another point on the floor that is coplanar with C and Q. [EX1, screen 14] Points B, R, F, and E are all coplanar with C and Q. 22. Points A, B, C, and F are noncoplanar points. Name another point in the room that is noncoplanar with A, B, and F. [EX1, screen 14] Points D, Q, R, S, and E are all noncoplanar with A, B, and F. Activity sheet 2, Page 7 of 7

21 Student Activity Sheet 3; use with Exploring Investigating points, lines, and planes Teacher Version 1. What parts of the box represent points? [EX2, screen 2] The corners, or vertices, of the box represent points. 2. What parts of the box represent lines? [EX2, screen 2] The edges of the box are segments, which are parts of lines. 3. What parts of the box represent planes? [EX2, screen 3] The sides, or faces, of the box represent parts of planes. 4. What does the box itself represent? [EX2, screen 3] The box represents a part of space. 5. What geometric object best represents the intersection of two lines? [EX2, screen 4] The intersection of two unique (different) lines is exactly one point. Activity sheet 3, Page 1 of 3

22 Student Activity Sheet 3; use with Exploring Investigating points, lines, and planes Teacher Version 6. How many lines intersect at each vertex of the box? [EX2, screen 4] Each vertex is the intersection of three unique lines. 7. What geometric figure represents the intersection of two planes? [EX2, screen 5] The intersection of two unique planes is exactly one line. 8. How many lines exist through any two points? [EX2, screen 6] Through any two points, there exists exactly one line. 9. Consider corners B, D, and F on the box, and answer the following questions. [EX2, screen 7] a. What plane or planes contain all three corners? Plane BDF contains all three corners. b. How many planes contain these three points? B, D, and F lie in exactly one plane. c. What is another name for this plane? Because points B, D, F and H are coplanar, the plane can be named BDH or BFH or DFH. 10. Complete the following sentence. [EX2, screen 9] Through any three noncollinear points there exists exactly one plane. 11. How many planes pass through three collinear points? [EX2, screen 10] Infinitely many planes pass through three collinear points. Activity sheet 3, Page 2 of 3

23 Student Activity Sheet 3; use with Exploring Investigating points, lines, and planes Teacher Version Using the terms provided, complete the following sentences. In sentences 14-16, assume that the two lines or planes are distinct and that they intersect. [EX2, screen 11] planes lines point plane collinear points two line three one noncollinear 12. A line is determined by exactly two points. 13. A plane is determined by exactly three noncollinear points. 14. Two lines intersect in exactly one point. 15. Two planes intersect in exactly one line. 16. Two intersecting lines lie in exactly one plane. Activity sheet 3, Page 3 of 3

24 Teacher Version Student Activity Sheet 4; use with Exploring Moving into hyperspace 1. Name a geometric object that represents each of the following dimensions. [EX3, screens 2-4] a. Zero dimension: point b. One dimension: line or line segment c. Two dimensions: plane or square d. Three dimensions: space or cube 2. Since the face of a 3-D cube is a 2-D square, what shape is the face of a hypercube, or 4-D cube? [EX3, screen 6] The face of a hypercube is a cube. 3. REEI INFFORRCCEE Complete the following table. You do not need to fill in any of the blank cells of the table that are shaded. Dimensions Object Number of vertices Number of lines Number of planes 0 point 1 1 line square cube hypercube Consider what a 5-dimensional object consists of! Activity sheet 4, Page 1 of 1

Geometry Reasons for Proofs Chapter 1

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