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Geometry Lesson 2-7: Proving Segment Relationships

Learn and practice writing proofs involving segment addition and congruence, utilizing Segment Addition Postulate and Segment Properties of Congruence. Apply postulates and theorems to solve problems in geometry. Homework exercises included.

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Geometry Lesson 2-7: Proving Segment Relationships

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  1. Geometry Lesson 2 – 7 Proving Segment Relationships Objective: Write proofs involving segment addition. Write proofs involving segment congruence.

  2. Postulate • Postulate 2.8 • The points on any line or line segment can be put into one-to-one correspondence with real numbers.

  3. Postulate • Segment Addition Postulate • If A, B, and C are collinear, then point B is between A and C if and only if AB + BC = AC

  4. Given: Prove:

  5. Complete the proof

  6. Segment Properties of Congruence • Reflexive • Symmetric • Transitive

  7. The route for a charity fitness run is shown. Checkpoint X and Z are the midpoints between the starting line and Checkpoint y and Checkpoint Y and the finish line F, respectively. If Checkpoint Y is the same distance from Checkpoint X and Z, prove that the route from Checkpoint Z to the finish line is congruent to the route from the starting line to the Checkpoint X.

  8. Given: Prove: (Or substitution)

  9. Homework • Pg. 145 1, 2, 4, 30 – 36

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