1. By Jeremy Cummings, Tarek Khalil, and Jai Redkar

2.  The measure of the exterior angle of a triangle is greater than the measure of either remote interior angle. The Logic Behind This Theorem: ∠ 1+ ∠ 2=180 ∠ 2+ ∠ 3+ ∠ 4=180 ∠ 1+ ∠ 2 = ∠ 2+ ∠ 3+ ∠ 4 ∠ 1= ∠ 3+ ∠ 4 ∠ 1> ∠ 3 ∠ 1> ∠ 4

3. How this would be done: 1. x <62 because of the exterior angle inequality theorem- 62° is the exterior angle and x is the remote interior 2. x > 0 because every angle in a triangle is greater than 0 3. So, the answer is 0<x<62 62° x Find the retrictions on x.

4. 125°5x-5 25° Write an inequality that states the restrictions on x: Do the problem and then continue to see work and answer. Work and Answer 25< 5x-5 <125 25<5x-5 5x-5<125 30<5x 5x<130 6<x x<26 6<x<26

5.  If two lines are cut by a transversal such that two alternate interior angles are congruent, the lines are parallel. ◦ Short Form: Alt. int. ∠ ' s ≅ => ∥ lines Given: ∠ 1 ≅ ∠ 2 Prove: y ∥ z

6.  If two lines are cut by a transversal such that two alternate exterior angles are congruent, the lines are parallel. ◦ Short Form: Alt. ext. ∠ ' s ≅ => ∥ lines Given: ∠ 1 ≅ ∠ 2 Prove: y ∥ z

7.  If two lines are cut by a transversal such that two corresponding angles are congruent, the lines are parallel. ◦ Short Form: Corr. ∠ ' s ≅ => ∥ lines Given: ∠ 1 ≅ ∠ 2 Prove: y ∥ z

8.  If two lines are cut by a transversal such that two interior angles on the same side of the transversal are supplementary, the lines are parallel. ◦ Short Form: Same side int. ∠ ' s suppl. => ∥ lines Given: ∠ 1 suppl ∠ 2 Prove: y∥z

9.  If two lines are cut by a transversal such that two exterior angles on the same side of the transversal are supplementary, the lines are parallel. ◦ Short Form: Same side ext. ∠ ' s suppl. => ∥ lines Given: ∠ 1 suppl ∠ 2 Prove: y∥z

10.  If two coplanar lines are perpendicular to a third line, they are parallel. Given: x ⊥ z and y ⊥ z Prove: x∥y

11.  Transversal t cuts lines k and n. m ∠ 1 = (148 - 3x)° and m ∠ 2 = (5x + 10)°. Find the value of x that makes k ∥ n. kn t 1 2 How to do this: 1.In order for k ∥ n, ∠ 1 has to be suppl. to ∠ 2 because of the theorem “Same side int. ∠ 's suppl. => ∥ lines.” 2.So, m ∠ 1 = (148 - 3x)° + m ∠ 2 = (5x + 10)°=180 because suppl. angles =180°. 3.Through algebra, 148-3x+5x+10=180 2x+158=180 2x=22 x=11

12. Given: BD bisects ∠ ABC BC ≅ CD Prove: CD ∥ BA Statements Reasons 1. Given 2. Given 3. ∠ ABD ≅ ∠ CBD3. If a ray bisects an ∠, then it divides the ∠ into 2 ≅ ∠ ’s. 4. ∠ CDB ≅ ∠ CBD 5. ∠ CDB ≅ ∠ ABD 5. Transitive 6. Alt. int. ∠ ’s ≅ => ∥ lines Write a 2- column proof and then continue to see the correct steps.

13. “9-1: Proving Lines Parallel.” Ekcsk12.org. Edwards-Knox Central School, n.d. Web. 18 Jan. 2011. “Perpindicular and Parallel Lines.” edHelper.com. edHelper.com, n.d. Web. 18 Jan. 2011. Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry for Enjoyment and Challange. New Edition. Evanston, Illinois: McDougal, Littell and Company, 2004. 216-18. Print.