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Unit 4H: Parallel Lines Study Guide Name: ___________________________ Period: _____ Due Date: _______ SHOW YOUR WORK FOR FULL CREDIT. NO WORK, NO CREDIT. NO WORK IN PEN. Targets Sample Rate your knowledge and understanding Struggle Copy an angle Construct Parallel Lines with Congruent Angles Understand congruent/ supplementary angle relationships Proving angle relationships with equations Need Help Not Too Bad Master Using a compass and straightedge copy the following angle: Given a line segment and point, not on the line, construct a parallel line using a compass and straight edge. Explain how you know the lines are parallel. Give an example of Alternate Interior Angles, Same Side Exterior and Corresponding Angles and state if congruent or supplementary. If the measure of angle a = 4 + 2p and b = 8p – 14, show that a and b are corresponding angles of parallel lines. Vocabulary Parallel: __________________________________________________________________________________________ Transversal: _______________________________________________________________________________________ Arc: ______________________________________________________________________________________________ Congruent: ________________________________________________________________________________________ Similar: ___________________________________________________________________________________________ Conditional Statement: ______________________________________________________________________________ Hypothesis: ____________________________________ Conclusion:_________________________________________ How do you know if two lines are parallel? _______________________________________________________________ _________________________________________________________________________________________________ Copy an Angle You can see a live animation at: http://www.mathopenref.com/constcopyangle.html Start with angle BAC that we will copy. Step 1: Make a point P that will be the vertex of the ________ _______________. Step 2: From P, draw a ray PQ. This will become one side of the new angle. Step 3: Place the compass on point ___, set to any convenient width. Step 4: Draw an ____ across both sides of the angle—create the points J and K shown. Step 5: Without changing the c______ width, place the compass point on P and draw a similar _____ there, creating point M as shown. Step 6: Set the compass on K and adjust its width to point J. Step 7: Without changing the compass width, move the compass to point ____ and draw an _____ across the first one, creating point ____ where _______ ________. Step 8: Draw a ray ___ from P through L and onwards—exact length in not important. DONE: <RPQ is congruent (equal in measure) to angle <BAC. Practice and copy the TWO angles below. Show all markings. Constructing a Parallel Line Through a Point. Live animation at http://www.mathopenref.com/constparallel.html (Parallel to line PQ, through point R) Step 1: Draw a line through point R that ________ the line PQ at any angle, forming the point J where it intersects the line PQ. Step 2: With the c_______ width set to about half the distance between point __ and J place the point on J, and draw an _____ across both lines (RJ and PQ). Step 3: Without adjusting the compass _______, move the compass to R and draw a similar ___ to the one in step 2. Step 4: Set compass width to the distance between where the lower arc crosses the two lines (one end at point T and the other at point K). Move the compass to where the upper arc crosses the line RJ (at point X). Step 5: Draw a straight _______ through points R and S. DONE: The line RS is parallel to the line PQ. Construct a line parallel to the line below that passes through the given point. Show All Markings. Parallel Lines cut by a transversal When two parallel lines are cut by a third line, the third line is called the ________________. In the example below, ________ angles are formed. There are several special pairs of angles formed from this figure. Line l ║m. Fill in the angle that matches for the given relationship. Circle whether congruent or supplementary. Vertical Angles: A & _____ Congruent Corresponding Angles: D & _____ Congruent Same-Side Interior Angles: C & _____ Congruent Same-Side Exterior Angles: H & _____ Congruent Alternate Interior Angles: D & _____ Congruent Alternate Exterior Angles: H & _____ Congruent A and G are ____________________ Angles H and E are a Linear Pair and so is C & _____ Supplementary Supplementary Supplementary Supplementary Supplementary Supplementary If E and F are a linear pair, and F = (s – 2)o and E = (3s + 2)o. Solve for s. _____ What is the measure of E? ______ What is the measure of F? ______ We can prove parallel lines, by knowing the angles relationships. Given the following information, determine which lines, if any, are parallel. If m6 m3 , then ___________________________________ If m4 m9 , then ___________________________________ If m4 m3 , then ___________________________________ If m4 m6 180 , then_______________________________ If m5 m8 , then ____________________________________ If m2 m3 180 , then _______________________________