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Geometry

Geometry. Agenda 1. ENTRANCE 2. go over practice 3. 3-2 Proving Lines Parallel 4. Practice Assignment 5. EXIT. Practice. Transitive Property. If a =b and b=c, then a=c. If a b and bc, then ac. If and , then . If 12 and 23, then 13.

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Geometry

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  1. Geometry • Agenda 1. ENTRANCE 2. go over practice 3. 3-2 Proving Lines Parallel 4. Practice Assignment 5. EXIT

  2. Practice

  3. Transitive Property • If a=b and b=c, then a=c. • If ab and bc, then ac. • If and , then . • If 12 and 23, then 13.

  4. Example #7 • Given: a||b • Prove: 13 1. a||b 2. 14 3. 43 4. 13

  5. Example #8 • Given: a||b • Prove: 1 supple 2 1. a||b 2. m2+m3=180 3. 31 4. m2+m1=180 5. 1 supple 2

  6. Chapter 3 3-2 Proving ________ Parallel

  7. Flowchart Proof • Proof with statements in boxes and reasons below them. ex: Given: 2x – 7 = 3 Prove: x = 5

  8. Postulate 3-2, Theorems 3-3 and 3-4 • If two lines and a transversal form: • Corresponding angles that are congruent • Alternate interior angles that are congruent • Same-side interior angles that are supplementary then the two lines are __________.

  9. Theorem 3-5 • If two lines are parallel to the same line, then they are parallel to each other. x||y and y||z therefore, x||z

  10. Theorem 3-6 • In a plane, if two lines are ___________ to the same line, then they are parallel to each other. gh and hj therefore, g||j

  11. Example #1 • Which lines (if any) must be parallel if: a. 26 b. 412 c. 10 supple 11 d. 38

  12. Example #2 • Find x for which m||n.

  13. Example #3 • Find x for which a||b.

  14. Example #4 • Find x for which p||q.

  15. Example #5 • Given: 32 Prove: m||n

  16. Example #6 • Given: at bt Prove: a||b (prove Thm 3-6)

  17. Practice • WB 3-2 # 2-13 • EXIT

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