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GEOMETRY

GEOMETRY. CHAPTER 1 1-1 Understanding points, lines and planes. Objectives. Students will be able to: Identify, name, and draw points, lines, segments, rays, and planes. Apply basic facts about points, lines, and planes . 1-1 Understanding lines .

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GEOMETRY

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  1. GEOMETRY CHAPTER 1 1-1 Understanding points, lines and planes

  2. Objectives • Students will be able to: • Identify, name, and draw points, lines, segments, rays, • and planes. • Apply basic facts about points, lines, and planes.

  3. 1-1 Understanding lines • The most basic figures in geometry are undefined terms, which cannot be defined by using other figures. The undefined terms point, line, and plane are the building blocks of geometry.

  4. K L M N Collinear Points • Points that lie on the same line are collinear. • Based on the definition. Which points are collinear? Which are not? K, L, and M are collinear. K, L, and N are noncollinear.

  5. Coplanar points • Points that lie on the same plane are coplanar. Otherwisethey are noncoplanar. • Example of Coplanar • All the points A, B, C, and D in the plane P are coplanar.

  6. Example 1 • Use the following figure to answer the following questions: • A) Name three collinear points Answer: D,E and F B) Name Coplanar points Answer: D,E,F and G C)Name a point that is noncollinear and a point that is not coplanar. • Answer: noncollinear is g and noncoplanar is h

  7. Segments and rays

  8. Example 2 • Draw a line segment with endpoints a and b • A B • Draw ray with endpoint e and pass through d • D E • Draw line gh • g h

  9. Postulates • A postulate, or axiom, is a statement that is accepted as true without proof. Postulates about points, lines, and planes help describe geometric properties.

  10. Example 3 Name a line that passes through two points Answer: cd Name a plane that contains three noncollinear points. Answer; plane ABC

  11. Intersecting lines • An intersection is the set of all points that two or more figures have in common. The next two postulates describe intersections involving lines and planes. Use a dashed line to show the hidden parts of any figure that you are drawing. A dashed line will indicate the part of the figure that is not seen.

  12. Example 4 • Representing Intersections • A. Sketch two lines intersecting in exactly one point. B. Sketch a figure that shows a line that lies in a plane.

  13. Homework • Page 9 13-21

  14. Closure • Today we saw about point, lines, lines segments and rays and how we label them. We also saw collinear and coplanar points. Tomorrow we are going to continue with lesson 1-2.

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