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Chapter 1 Foundations for Geometry

In this chapter, we delve into the foundational concepts of geometry, focusing on undefined terms such as points, lines, and planes. We explore essential properties, including collinearity and coplanarity. The chapter introduces key postulates that describe the relationships between these geometric elements, such as the existence of a line through any two points and a plane through any three non-collinear points. Additionally, we discuss the intersection of lines and planes, essential for understanding geometric relationships. Practice problems are provided to reinforce these concepts.

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Chapter 1 Foundations for Geometry

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  1. Chapter 1Foundations for Geometry

  2. 1-1: Understanding Points, lines, & planes

  3. Undefined terms

  4. More terms • Points that lie in the same planeare coplanar. • Pointsthat lie on the same line are collinear.

  5. Segments

  6. Rays

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

  8. Postulates: points, lines, & planes • Through any 2points there is exactly one line. • Through any 3 non-collinear points there is exactly one plane containing them. • If 2 points lie on a plane, then the line containing those points lies in the plane.

  9. Postulate: Intersection of lines & planes • If 2 lines intersect, then they intersect in exactly one point. • If 2 planes intersect, then they intersect in exactly one line.

  10. HW Pg. 9 #4-34 even (omit 30)

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