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Math 11 Unit 2 - Geometry Day 2 Notes Exploring Parallel Lines Intro Activity Transversal – a line that intersects two or more other lines at distinct points. Transversal crossing two lines this Transversal crosses two parallel lines ... and this one cuts across three lines When a transversal intersects two parallel lines, how are the angle measures related? Interior angles – any angles formed by a transversal and two parallel lines that lie inside the parallel lines. (see Ð3, Ð4, Ð5 and Ð6 ) 1. Two interior angles on the same side of the transversal will add to 180°. (IASST = 180o) 2. Two interior angles on alternate sides of the transversal will be equal. (alt. int. <s =) Matty 2012 Math 11 Unit 2 - Geometry Day 2 Notes Correspondingl angles - one interior angle and one exterior angle that are non-adjacent but on the same side of the transversal. (see Ð1 and Ð5, Ð4 and Ð8, Ð2 and Ð6, Ð3 and Ð7 ) 3. Pairs of corresponding angles are always equal. Vertically opposite angles - the angles opposite each other when two lines cross. (see Ð1 and Ð3, Ð2 and Ð4, Ð5 and Ð7, Ð6 and Ð8 ) 4. Pairs of vertically opposite angles are always equal. ***These 4 above laws are crucial to understand for the rest of the unit** Activity #2: Grab a laptop in a group of two and check out the following websites and experiment with the animations to help you understand the terms and rules of parallel lines: 1. Terms: http://tube.geogebra.org/m/153296 2. More on terms and Relationships: http://tube.geogebra.org/m/575951 Now try some of these examples and determine the unknown angle measurements: 1. x w y Ðx= Ðw= 120° Ðy= Matty 2012 Math 11 Unit 2 - Geometry 55° Day 2 Notes Ða= 2. Ðb= d a Ðc= e f b 112° c Ðd = Ðe= Ðf= 3. Ð b= d Ð c= c b Ð d= 48° e g Ð e= f Ð f= Ð g= Assignment 2.2 1. Complete the sentences with the correct word: always, sometimes, or never. Parallel lines are __________________________ the same distance apart. Parallel lines ______________________________ intersect. Parallel lines are ___________________________ cut by a transversal. Parallel lines that are cut by a transversal _____________________ form right angles. Matty 2012 Math 11 Unit 2 - Geometry Day 2 Notes 2. Use a pencil to thicken one set of parallel lines in this pattern. 3. Determine the measure of ABF. 4. Determine the values of a, b, and c. 5. Are BD and FE parallel? Explain how you know. d y 6. Use the following figure to the right to answer questions: t a) Is line d a transversal? Why or why not? b) Is line y a transversal? c) Is line t a transversal? Why or why not? d) Is line r a transversal? Matty 2012 r