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Splash Screen. 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.

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Splash screen

Splash Screen


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

Lesson Menu


5 minute check 1

What is the value ofx2 +3yz if x = 3, y = 6, and z = 4?

A.27

B.33

C.72

D.81

5-Minute Check 1


5 minute check 2

A.–6

B.

C.2

D.6

Solve 2(x – 7) = 5x + 4.

5-Minute Check 2


5 minute check 3

Which is a solution of 3x + 4y = 14?

A.(–3, 4)

B.(–2, 5)

C.(1, 3)

D.(2, 3)

5-Minute Check 3


5 minute check 4

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


5 minute check 5

A.B.

C.D.

Graph y = 3x + 2.

5-Minute Check 5


5 minute check 6

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


Splash screen

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


Then now

You used basic geometric concepts and properties to solve problems.

  • Identify and model points, lines, and planes.

  • Identify intersecting lines and planes.

Then/Now


Vocabulary

  • definition

  • defined term

  • space

  • undefined term

  • point

  • line

  • plane

  • collinear

  • coplanar

  • intersection

Vocabulary


Concept

Concept


Example 1

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.

Name Lines and Planes

A. Use the figure to name a line containing point K.

Example 1


Example 11

Answer: The plane can be named as plane B.

You can also use the letters of any three noncollinearpoints to name the plane.plane JKMplane KLMplane JLM

Name Lines and Planes

B. Use the figure to name a plane containing point L.

Example 1


Example 12

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


Example 1a

A.line X

B.line c

C.line Z

D.

A. Use the figure to name a line containing the point X.

Example 1a


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 1b


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


Example 21

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


Example 2a

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


Example 2b

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


Example 3

Draw Geometric Figures

Draw a surface to represent plane R and label it.

Example 3


Example 31

Draw Geometric Figures

Draw a line anywhere on the plane.

Example 3


Example 32

Draw Geometric Figures

Draw dots on the line for point A and B. Label the points.

Example 3


Example 33

Draw Geometric Figures

Example 3


Example 34

Draw Geometric Figures

Draw dots on this line for point D and E. Label the points.

Example 3


Example 35

Draw Geometric Figures

Label the intersection point of the two lines as P.

Example 3


Example 36

Draw Geometric Figures

Answer:

Example 3


Example 37

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


Example 3a

A.B.C.D.

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 3a


Example 3b

Example 3b


Example 3b1

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


Example 41

Interpret Drawings

B. Name three points that are collinear.

Answer: Points A, B, and D are collinear.

Example 4


Example 42

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


Example 43

Interpret Drawings

Answer: The two lines intersect at point A.

Example 4


Example 4a

A. How many planes appear in this figure?

A.one

B.two

C.three

D.four

Example 4a


Example 4b

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


Example 4c

C. Are points X, O, and R coplanar?

A.yes

B.no

C.cannot be determined

Example 4c


Example 4d

A.point X

B.point N

C.point R

D.point A

Example 4d


End of the lesson

End of the Lesson


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