Download Name October 19, 2006

Name ___________________________
Team ___________________________
October 19, 2006
Do Now
Read the following statements:
1. The sun came up this morning.
The sun came up the day before that.
The sun came up the day before that.
.
.
Therefore, the sun comes up every day, and will come up tomorrow
too.
Is this a logical conclusion? Was the conclusion made using inductive or deductive
reasoning?
2. How about this argument?
It rained this morning.
It rained the day before that.
It rained the day before that?
.
.
.
Therefore, it rains everyday, and will rain tomorrow too.
Is this logical?
3. How are these two arguments different?
Group Work
October 19, 2006
List all members of the group:
Directions:
Have one group member read the directions to each group member
The objective of today’s activity is to use inductive and deductive reasoning to prove two
conjectures: one which we have already learned and one which we have not.
You will each perform the activity, but work together, as the conjectures you make will
depend on the results of all group members.
You will receive both a group and individual grade.
When you are finished, please place all materials in the envelop. Make sure everything is
cleaned up.
Group Work
October 19, 2006
List all members of the group:
Directions:
Have one group member read the directions to each group member
The objective of today’s activity is to use inductive and deductive reasoning to prove two
conjectures: one which we have already learned and one which we have not.
You will each perform the activity, but work together, as the conjectures you make will
depend on the results of all group members.
You will receive both a group and individual grade.
When you are finished, please place all materials in the envelop. Make sure everything is
cleaned up.
Name _____________________
Team _____________________
October 19, 2006
Task #1
To prove the vertical angles conjecture using both inductive and deductive reasoning.
Vertical Angles Conjecture: If two angles are vertical angles, then the angles are
______________ (means they have the same measurement)
Part I: Prove using inductive reasoning
Step #1: Using a ruler, draw two intersecting lines the patty paper. Label them angles 14. The following is a couple of examples:
Step #2: Fold the patty paper on the vertex so that angles 1 and 3 lie over each other.
What do you notice about their measurements? _________________________________
Step #3: Repeat step #2 with angles 2 and 4. What do you notice about their
measurements? __________________________________________________________
Did your group members notice the same thing? ________________________________
Step #4: Measure and record each angle with a protractor.
m< 1 = ______________
m < 3 = ______________
m <2 = ______________
m <4 = ______________
What do you notice about the measurements of each pair of vertical angles?
____________________________
Did your group members notice the same thing?_____________.
What conjecture can you make about vertical angles based on the above observations:
Do you think this conjecture would hold true regardless of the angles formed by the
intersecting lines in step #1? Please Explain.
Do you think you would have been able to make that same conjecture if you performed
the above experiment with only one pair of intersecting lines (without considering the
results of your group members)? Why or why not?
Part II: Prove using deductive reasoning
Fill in the blanks:
m <1 + m < 2 = _________. This is because they are ____________________ angles.
m <2 + m<3 = ________________.
Therefore, __________________________________________. This is because of the
________________ property.
Use the subtraction property to subtract m <2 from both sides. The conclusion you can
make is: ________________________________________
Is this the same or different than the conjecture you made previously?
Which conclusion do you think is stronger; the one you made using inductive reasoning
or the one you made using deductive reasoning? Why?
Bonus: The converse of the conjecture states that if two angles are congruent (i.e. have
the same measurements), then they are vertical. Is the converse true? Why or why not? If
you think it is true, can you prove it? If you don’t think it’s true, can you disprove it?
Task #2: Use inductive reasoning to determine a new conjectures.
Step #1: On the index card, use a ruler to draw a pair of parallel lines. Label them k and l
as follows:
Step #2: Draw a line intersecting the two. Label it line m. (*Note: This line is called the
transversal) Each group member should try to make the lines intersect at different
angles. Then label the angles. A couple of examples are:
m
m
Step #2: Place a piece of patty paper over the set of angles 1, 2, 3, and 4. Copy the two
intersecting lines, m and L, and the 4 angles, 1 through4, on the patty paper.
Step #3: Slide the patty paper down to the intersection of lines m and k (where the two
lines meet).
Step #4: Compare angles 1 through 4 with angles 5 through 8. What do you notice? List
all pairs of congruent angles:
Did everyone in your group make the same conclusion?
Step #5 Measure and record each angle with a protractor.
m <1
m<2
m<3
m<4
m< 5
m< 6
m <7
m <8
Do you get the same results?
Did everyone in your group make the same conclusion?
What conjectures can you make (*Note: Angles 1 and 5, 3 and 7, 2 and 6, and 4 and 8 are
called corresponding angles)?
Conjecture: Corresponding angles are ___________________________
Did the different angle measurements that each of your group members had impact the
conjecture?
Are you absolutely certain about the conjectures you made using inductive reasoning in
the above two tasks?
Are you absolutely certain about the conjectures you made using deductive reasoning in
the above two tasks?
How is this conjecture different than the ones you made during the do now?