4 4 proving lines parallel
- 1. Proving Lines Parallel You will learn to identify conditions that produce parallel lines. Reminder: In Chapter 1, we discussed “if-then” statements (pg. 24). Within those statements, we identified the “__________” and the “_________”. hypothesis conclusion I said then that in mathematics, we only use the term “if and only if” if the converse of the statement is true.
- 2. Proving Lines Parallel Postulate 4 – 1 (pg. 156): IF ___________________________________, THEN ________________________________________. two parallel lines are cut by a transversal each pair of corresponding angles is congruent The postulates used in 4 - 4 are the converse of postulates that you already know. COOL, HUH? 4 – 4, Postulate 4 – 2 (pg. 162): IF ________________________________________, THEN ____________________________________. each pair of corresponding angles is congruent two parallel lines are cut by a transversal
- 3. Proving Lines Parallel Postulate 4-2 In a plane, if two lines are cut by a transversal so that a pair of corresponding angles is congruent, then the lines are _______.parallel If 1 2, then _____a || b 1 2 a b
- 4. Proving Lines Parallel Theorem 4-5 In a plane, if two lines are cut by a transversal so that a pair of alternate interior angles is congruent, then the two lines are _______.parallel If 1 2, then _____a || b 1 2 a b
- 5. Proving Lines Parallel Theorem 4-6 In a plane, if two lines are cut by a transversal so that a pair of alternate exterior angles is congruent, then the two lines are _______.parallel If 1 2, then _____a || b 1 2 a b
- 6. Proving Lines Parallel Theorem 4-7 In a plane, if two lines are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the two lines are _______.parallel If 1 + 2 = 180, then _____a || b1 2 a b
- 7. Proving Lines Parallel Theorem 4-8 In a plane, if two lines are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the two lines are _______.parallel If a t and b t, then _____a || b a b t
- 8. Proving Lines Parallel Concept Summary We now have five ways to prove that two lines are parallel. Show that a pair of corresponding angles is congruent. Show that a pair of alternate interior angles is congruent. Show that a pair of alternate exterior angles is congruent. Show that a pair of consecutive interior angles is supplementary. Show that two lines in a plane are perpendicular to a third line.
- 9. Proving Lines Parallel Identify any parallel segments. Explain your reasoning. G A Y D R 90° 90° therefore, GAlar toperpendicubothareand RDGY 8.-4TheorembyRDGY
- 10. Proving Lines Parallel EB ST (6x - 26)° (2x + 10)° (5x + 2)° Find the value for x so BE || TS. ES is a transversal for BE and TS. BES and EST are _________________ angles.consecutive interior If m BES + m EST = 180, then BE || TS by Theorem 4 – 7. m BES + m EST = 180 (2x + 10) + (5x + 2) = 180 7x + 12 = 180 7x = 168 x = 24 Thus, if x = 24, then BE || TS.