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Understanding Segments, Rays, and Theorems in Geometry

Dive into the fundamentals of geometry with our comprehensive lesson on segments and rays. This guide outlines key theorems, postulates, formulas, and essential properties you'll need for quizzes and tests. Learn about the Segment Addition Postulate, congruent segments, midpoint definitions, and the Distance Formula. Each lesson is designed to build your knowledge and confidence in geometry, complete with practice problems and homework assignments. Whether you're a student or a teacher, this resource is a valuable tool for mastering geometric concepts.

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Understanding Segments, Rays, and Theorems in Geometry

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  1. Index Card • Let’s start our stack of Theorems, Postulates, Formulas, and Properties that you will be able to bring into a quiz or test. • Whenever I want you to add to your Theorem or Postulates I will set the background to bright yellow Lesson 1-1 Point, Line, Plane

  2. 12 AB = AC + CB = 4 + 8 = 12 The Segment Addition Postulate Postulate: If C is between A and B, then AC + CB = AB. The length of a line segment is equal to the sum of its parts. If AC = 4 , CB = 8 then Example: 8 4 Lesson : Segments and Rays

  3. If numbers are equal the objects are congruent. AB: the segment AB ( an object ) AB: the distance from A to B ( a number ) Congruent Segments Definition: Segments with equal lengths. (congruent symbol: ) Congruent segments can be marked with dashes. Correct notation: Incorrect notation: Lesson 1-2: Segments and Rays

  4. Midpoint Definition: A point that divides a segment into two congruent segments Formulas: On a number line, the coordinate of the midpoint of a segment whose endpoints have coordinates a and b is . Lesson 1-2: Segments and Rays

  5. Midpoint In a coordinate plane for a line segment whose endpoints have coordinates and . The midpoint is given by: . Lesson 1-2: Segments and Rays

  6. Midpoint Formula In a coordinate plane for a line segment whose endpoints have coordinates and The midpoint is given by: . Lesson 1-2: Segments and Rays

  7. Practice • Find the midpoint between (7, -2) and (-4, 8). Lesson 1-2

  8. Segment Bisector Definition: Any segment, line or plane that divides a segment into two congruent parts is called segment bisector. Lesson 1-2: Segments and Rays

  9. The Distance Formula

  10. The Distance Formula

  11. The Distance Formula The distance d between any two points with coordinates and is given by the formula d = . Lesson 1-2

  12. d = d = d = The Distance Formula Find the distance between (-3, 2) and (4, 1) Example: x1 = -3, x2 = 4, y1 = 2 , y2 = 1 Lesson 1-2

  13. Practice • Find the distance between (3, 2) and (-1, 6). Lesson 1-2: Formulas

  14. Homework • Pg. 19 # 8, 12, 16, 19, 21 • Pg 20 # 24, 26, 32 • Pg 21 # 52 Lesson 1-2: Formulas

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