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Lesson Menu 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

5-Minute Check 1 A.27 B.33 C.72 D.81 What is the value of x 2 + 3yz if x = 3, y = 6, and z = 4?

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

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

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

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

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

CCSS 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.

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

Vocabulary Undefined Term – words, usually understood, that readily are not formally explained by means of more basic words and concepts. The basic undefined terms of geometry are point, line and plane.

Concept

Collinear – points that lie on the same line. Noncollinear – points that do not lie on the same line Coplanar – points that lie in the same plane Noncoplanar – points do not lie in the same plane Intersection – set of points that two or more figures have in common

Definitions and Defined Terms – are explained using undefined terms and/or other defined terms Space – a boundless, three-dimensional set of all points. Space can contain lines and planes.

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

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

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

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

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

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

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

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

Example 3 Draw Geometric Figures

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

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

Example 3 Draw Geometric Figures Answer:

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

Draw and label a figure for each relationship. Lines AB and CD intersect at E for A(-2, 4), B(0, -2), C(-3, 0), D(3, 3) on a coordinate plane. Point F is coplanar with these points, but not collinear with line AB or line CD.

1)Point J(-4, 2), K(3, 2) and L are collinear 2) Line p lies on plane N and contains point L

A.B. C.D. Example 3a 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.

Example 3b

A.B. C.D. Example 3b

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

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

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

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

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

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

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

End of the Lesson