Dr. Antonio Quesada – Director, Project AMP
Project AMP
Angles and Parallel Lines
1.
Name ________________
Consider the drawing below.
m < 1 = ______
m < 2 = ________
Using a protractor, measure
each angle and record your m < 3 = ______
m < 4 = ________
answers at the right.
NOTE: m//n and t is called
m < 5 = ______
m < 6 = ________
a transversal.
m < 7 = ______
m < 8 = ________
t
1
2
3
4
5
6
7
m
8
n
2.
Now create a similar drawing of two parallel lines and a transversal using Cabri Geometry or
Geometer Sketchpad. You will need to locate and label
enough points to name each angle. Using
your software, measure each angle. Record your results below.
____________
____________
____________
____________
____________
____________
____________
____________
3.
Continuing with your computer drawing, select and move the transversal line so that you get
different measures of angles. What conclusions can you make?
Dr. Antonio Quesada – Director, Project AMP
Project AMP
4.
Create a new drawing of two lines which are NOT parallel but are both
crossed by a
transversal line. Again you will need to locate and label
enough points to name each angle. Using
your software, measure each angle and record your data below.
____________
____________
____________
____________
____________
____________
____________
____________
What conclusions can you now make?
5.
Refer back to the diagram in example 1.
The following pair of angles are called CORRESPONDING angles:
2&6 4&8 1&5 3&7
The following pair of angles are called ALTERNATE INTERIOR angles:
3&6 4&5
The following pair of angles are called ALTERNATE EXTERIOR angles:
1&8 2&7
Discuss and state why you think these angles were so named?
Dr. Antonio Quesada – Director, Project AMP
Project AMP
r
x
t
c
k
1
b
p
a
2
6.
3
Consider this diagram.
Name all pairs of corresponding angles.
____________
____________
Name all pairs of
alternate interior angles
____________
____________
____________
alternate exterior angles.
____________
____________
____________
Name all pairs of vertical angles.
____________
6. (cont)
____________
____________
____________
What other types of angles can you identify?
_________________________________________________________________
If line 1 // 2 and m < b = 38o, what other angles can you determine?
m < b = 38o ____________
____________
____________
____________
____________
____________
If m < b = 42o and m < x = 39o, can you make any conclusions?
____________
Dr. Antonio Quesada – Director, Project AMP
Project AMP
7.
Refer back to the diagram from #6. It is given that line 1 // 2.
a) If < x = 5 (x + 3) and < a = 2 (3x - 11), find angles x and a.
b) If < c= 5x - 43 and < k = 3x + 23, find angles c and k.
8.
You are driving in a car on Drexel Road. Soon you will cross Randall then
Holiday
roads which are parallel. All roads are straight. As you stop at
the intersection of Drexel and
Randall, you must turn your head 74o to
the right to see if there is any traffic.
a. Sketch and label these roads below.
b. What angle must you turn your head to the left? ________
c. When you get to the intersection of Drexel and
Holiday, what angle must you turn your head
to the left? to the right?
d. Why is this?
________
________