1. Splash Screen

2. What is the value of x2 + 3yz if x = 3, y = 6, and z = 4?
B. 33
C. 72
D. 81
5-Minute Check 1

3. Solve 2(x – 7) = 5x + 4.
A. –6 B.
C. 2
D. 6
5-Minute Check 2

4. Which is a solution of 3x + 4y = 14?
B. (–2, 5)
C. (1, 3)
D. (2, 3)
5-Minute Check 3

5. Factor 9x2 – 25y2. A. (3x – 5y)2 B. (3x + 5y)2 C. (3x + 5y)(3x – 5y)
D. (9x + 5y)(x – 5y)
5-Minute Check 4

6. Graph y = 3x + 2.
A. B.
C. D.
5-Minute Check 5

7. Which of the following equations is a quadratic equation?
A. 4x = 2
B. 5x + 2y = 13
C. 6x2 – 3x = 16
D. 5x3 – x2 + 2 = 0
5-Minute Check 6

8. Mathematical Practices 4 Model with mathematics.
Content Standards
G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
Mathematical Practices
4 Model with mathematics.
6 Attend to precision.
CCSS

9. You used basic geometric concepts and properties to solve problems.
Identify and model points, lines, and planes.
Identify intersecting lines and planes.
Then/Now

10. undefined term definition defined term space point line plane
collinear
coplanar
intersection
Vocabulary

11. Concept

12. A. Use the figure to name a line containing point K.
Name Lines and Planes
A. 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.
Example 1

13. B. Use the figure to name a plane containing point L.
Name Lines and Planes
B. Use the figure to name a plane containing point L.
You can also use the letters of any three noncollinear points to name the plane. plane JKM plane KLM plane JLM
Answer: The plane can be named as plane B.
Example 1

14. Name Lines and Planes
The letters of each of these names can be reordered to create other acceptable names for this plane. For example, JKM can also be written as JMK, MKJ, KJM, KMJ, and MJK. There are 15 different three-letter names for this plane.
Example 1

15. A. Use the figure to name a line containing the point X.
A. line X
B. line c
C. line Z D.
Example 1a

16. B. Use the figure to name a plane containing point Z.
A. plane XY
B. plane c
C. plane XQY
D. plane P
Example 1b

17. A. Name the geometric shape modeled by a 10  12 patio.
Model Points, Lines, and Planes
A. Name the geometric shape modeled by a 10  12 patio.
Answer: The patio models a plane.
Example 2

18. B. Name the geometric shape modeled by a button on a table.
Model Points, Lines, and Planes
B. Name the geometric shape modeled by a button on a table.
Answer: The button on the table models a point on a plane.
Example 2

19. A. Name the geometric shape modeled by a colored dot on a map used to mark the location of a city.
A. point
B. line segment
C. plane
D. none of the above
Example 2a

20. B. Name the geometric shape modeled by the ceiling of your classroom.
A. point
B. line segment
C. plane
D. none of the above
Example 2b

21. Draw a surface to represent plane R and label it.
Draw Geometric Figures
Draw a surface to represent plane R and label it.
Example 3

22. Draw a line anywhere on the plane.
Draw Geometric Figures
Draw a line anywhere on the plane.
Example 3

23. Draw dots on the line for point A and B. Label the points.
Draw Geometric Figures
Draw dots on the line for point A and B. Label the points.
Example 3

24. Draw Geometric Figures
Example 3

25. Draw dots on this line for point D and E. Label the points.
Draw Geometric Figures
Draw dots on this line for point D and E. Label the points.
Example 3

26. Label the intersection point of the two lines as P.
Draw Geometric Figures
Label the intersection point of the two lines as P.
Example 3

27. Draw Geometric Figures
Answer:
Example 3

28. Draw Geometric Figures
Answer:
Example 3

29. Draw Geometric Figures
Answer:
There are an infinite number of points that are collinear with Q and R. In the graph, one such point is T(1, 0).
Example 3

30. Draw Geometric Figures
Answer:
There are an infinite number of points that are collinear with Q and R. In the graph, one such point is T(1, 0).
Example 3

31. A. Choose the best diagram for the given relationship
A. Choose the best diagram for the given relationship. Plane D contains line a, line m, and line t, with all three lines intersecting at point Z. Also, point F is on plane D and is not collinear with any of the three given lines.
A. B C. D.
Example 3a

32. Example 3b

33. A. B.
C. D.
Example 3b

34. A. How many planes appear in this figure?
Interpret Drawings
A. How many planes appear in this figure?
Answer: There are two planes: plane S and plane ABC.
Example 4

35. B. Name three points that are collinear.
Interpret Drawings
B. Name three points that are collinear.
Answer: Points A, B, and D are collinear.
Example 4

36. C. Are points A, B, C, and D coplanar? Explain.
Interpret Drawings
C. Are points A, B, C, and D coplanar? Explain.
Answer: Points A, B, C, and D all lie in plane ABC, so they are coplanar.
Example 4

37. Answer: The two lines intersect at point A.
Interpret Drawings
Answer: The two lines intersect at point A.
Example 4

38. A. How many planes appear in this figure?
A. one
B. two
C. three
D. four
Example 4a

39. B. Name three points that are collinear.
A. B, O, and X
B. X, O, and N
C. R, O, and B
D. A, X, and Z
Example 4b

40. C. Are points X, O, and R coplanar?
A. yes
B. no
C. cannot be determined
Example 4c

41. A. point X
B. point N
C. point R
D. point A
Example 4d

42. End of the Lesson