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3 3 Proving Lines are Parallel Notes Brocket 13-14.notebook
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October 01, 2013
Topic: Proving Lines Parallel
are parallel?
Have homework outFill in assignment sheetCheck out a calculator if neededGet sheets from back table
6 9/30 10/1
Guided
Notes-
Section
3.3
Notes
7 9/30 10/1 W.S. 3.3 Cw/HW 10
3 3 Proving Lines are Parallel Notes Brocket 13-14.notebook
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Warm up - Parallel Lines and Transversals
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Warm-up answers
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Homework Answers
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Construction activity - Proving Lines parallel
1) Draw line l across the bottom of the blank sheet of paper provided. Label two points A and B on the linelike I have done below.
2) Using a protractor, construct two 45 degree angles with vertices A and B, both opening to the right. Label the points you used to make the 45 degree angles C and D,and draw lines AC and BD.
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3) Now construct two 90 degree angles with vertices A and B, above line AB, and using line AB as one ofthe sides. Mark the two points you used two make your right angles E and F, respectively. Connect points A and E, and B and F, with a dashed line segment.
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l
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3 3 Proving Lines are Parallel Notes Brocket 13-14.notebook
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4) Now rotate your paper so the AB is vertical with B above A as shown. Using E and Fas your vertex, and AE and FB as a side of the angle, make two more right angles openingtowards AB. Draw two new dashed segments of the right angles so that they intersect lines AC and BD.Label the points of intersection G and H, respectively.
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5) If AC and BD had the same slopes, then the lines would be ___________________.
6) How could we find the slopes of lines AC and BD?
7) Using a ruler, measure the lengths of AE, EC, BF, and FH in millimeters. Then, find the slopes ofAC and BD?
8) Slope of AC= _______________, Slope of BD = _______________
9) How close were your slopes to being equal? _____________________
10) Can we conclude that AC is parallel to BD?_________________
11) What kind of angles are the two angles we constructed that are 45 degrees. _______________
12) Finish this statement: If two lines are cut by a transversal such that __________________angles are congruent, then the two lines are _____________________.
l l
l
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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150°
3 3 Proving Lines are Parallel Notes Brocket 13-14.notebook
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There are 6 ways to prove that lines are parallel if cut by a transversal.
1) Show that Corresponding angles are congruent2) Show that Alternate interior angles are congruent3) Show that Alternate exterior angles are congruent4) Show that Same-side interior angles are supplementary5) Show that two lines are perpendicular to the same line6) Show two lines are parallel to the same line
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Example 1
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Example 2
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Example 3
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What value of x proves the lines are parallel and what are the sizes of angles 1 and 2?
Example 4
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Example 5
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Homework: W.S 3.3
Quiz 3.1-3.3 Next class
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