# [PDF] Big Ideas Math Geometry PDF

Going Back To KINDERGARTEN For A Day!
Going Back To KINDERGARTEN For A Day!

### Big Ideas Math

Points, Lines, and Planes

Essential Question Essential Question How can you use dynamic geometry software to visualize geometric concepts?

Using Dynamic Geometry Software

Work with a partner. Use dynamic geometry software to draw several points.

Also, draw some lines, line segments, and rays. What is the difference between a line, a line segment, and a ray?

Intersections of Lines and Planes

Work with a partner.

a. Describe and sketch the ways in which two lines can intersect or not intersect.

Give examples of each using the lines formed by the walls, floor, and ceiling in your classroom.

b. Describe and sketch the ways in which a line and a plane can intersect or not intersect.

Give examples of each using the walls, floor, and ceiling in your classroom.

c. Describe and sketch the ways in which two planes can intersect or not intersect.

Give examples of each using the walls, floor, and ceiling in your classroom.

Exploring Dynamic Geometry Software

Work with a partner. Use dynamic geometry software to explore geometry.

Use the software to find a term or concept that is unfamiliar to you.

Then use the capabilities of the software to determine the meaning of the term or concept.

What You Will Learn What You Will Learn

Name points, lines, and planes.
Name segments and rays.
Sketch intersections of lines and planes.
Solve real-life problems involving lines and planes.

Using Undefined Terms

In geometry, the words point, line, and plane are undefined terms.

These words do not have formal definitions, but there is agreement about what they mean.

Core Concept

Undefined Terms: Point, Line, and Plane Point A point has no dimension. A dot represents a point.

Line A line has one dimension. It is represented by a line with two arrowheads, but it extends without an end.

Through any two points, there is exactly one line.

You can use any two points on a line to name it.

Plane A plane has two dimensions.

It is represented by a shape that looks like a floor or a wall, but it extends without end.

Through any three points not on the same line, there is exactly one plane.

You can use three points that are not all on the same line to name a plane.

#### Solving Real-Life Problems

Modelling with Mathematics

The diagram shows a molecule of sulfur hexafluoride, the most potent greenhouse gas
in the world. Name two different planes that contain line r.

SOLUTION

Understand the Problem In the diagram, you are given three lines, p, q, and r, that intersect at point B.

You need to name two different planes that contain line r.

Make a Plan The planes should contain two points on line r and one point not on line r.

Solve the Problem Points D and F are online r. Point E does not lie on line r.

So, plane DEF contains line r. Another point that does not lie on line r is C. So, plane CDF contains line r.

Note that you cannot form a plane through points D, B, and F. By definition, three points that do not lie on the same line form a plane. Points D, B, and F are collinear, so they do not form a plane.

Look Back The question asks for two different planes.

You need to check whether plane DEF and plane CDF are two unique planes or if the same plane is named differently.

Because point C does not lie on plane DEF, plane DEF and plane CDF are different planes.

WRITING Your friend is having trouble understanding the Midpoint Formula.

a. Explain how to find the midpoint when given the two endpoints in your own words.

b. Explain how to find the other endpoint when given one endpoint and the midpoint in your own words.

PROBLEM-SOLVING

In baseball, the strike zone is the region a baseball needs to pass through for the umpire to declare it a strike when the batter does not swing.

The top of the strike zone is a horizontal plane passing through the midpoint of the top of the batter’s shoulders and the top of the uniform pants when the player is in a batting stance.

Find the height of T. (Note: All heights are in inches.)

### Chapters List

 S.r No. Chapter Chapter Name 1. Chapter 1 Basics of Geometry 2. Chapter 2 Reasoning and Proofs 3. Chapter 3 Parallel and Perpendicular Lines 4. Chapter 4 Transformations 5. Chapter 5 Congruent Triangles 6. Chapter 6 Relationships Within Triangles 7. Chapter 7 Quadrilaterals and Other Polygons 8. Chapter 8 Similarity 9. Chapter 9 Right Triangles and Trigonometry 10. Chapter 10 Circles 11. Chapter 11 Circumference, Area, and Volume 12. Chapter 12 Probability
 Author – Language English No. of Pages 56 PDF Size 10 MB Category Mathematics Source/Credits static.bigideasmath.com