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Key Concept: Undefined Terms Example 1: Name Lines and Planes Five-Minute Check CCSS Then/Now New Vocabulary Key Concept: Undefined Terms Example 1: Name Lines and Planes Example 2: Real-World Example: Model Points, Lines, and Planes Example 3: Draw Geometric Figures Example 4: Interpret Drawings Lesson Menu

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

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

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

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

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

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

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

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

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

Concept

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

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

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

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

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

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

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

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

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

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

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

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

Draw Geometric Figures Example 3

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

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

Draw Geometric Figures Answer: Example 3

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

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

Example 3b

A. B. C. D. Example 3b

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

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

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

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

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

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

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

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

End of the Lesson