Download Unit 4H: Parallel Lines Study Guide

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 m6  m3 , then ___________________________________
If m4  m9 , then ___________________________________
If m4  m3 , then ___________________________________
If m4  m6  180 , then_______________________________
If m5  m8 , then ____________________________________
If m2  m3  180 , then _______________________________