Download PART 1 (Consecutive Angles)

GEOMETRY
INVESTIGATION
Consecutive Angles
Objective: In this investigation you will learn about consecutive angles.
PART 1: Consecutive Interior Angles
Step 1: In the space below are two parallel lines. (Again, trust me on this one.) Draw a transversal through
the parallel lines.
Step 2: Label the eight angles created “1” through “8”
Step 3: There are two pairs of consecutive interior angles. Label them below:
Angle______ is a consecutive interior angle with angle _____.
Angle ______is a consecutive interior angle with angle _____.
Step 4: Choose one pair of consecutive angles to work with.
What pair are you using? <
and <
Measure each angle with a protractor. Write their measurements here:
What do you notice?
Step 5: Repeat Step 4 with your next pair of consecutive interior angles.
Step 6: Write your conjecture about the measures of consecutive interior angles below.
Conjecture: If two parallel lines are cut by a transversal, then the measures of
consecutive interior angles are ________________________________.
GEOMETRY
INVESTIGATION
Consecutive Angles
Objective: In this investigation you will learn about consecutive angles.
PART 2: Lines that are NOT parallel
Step 1: In the space below are two lines that are NOT parallel. (Normally, you can’t trust my
drawing, but explain from the drawing why you can probably trust this one.)
Step 2: Draw a transversal and label the angles 1 through 8 (in the same manner/order that you
labeled the angles of the parallel lines cut by a transversal on the first page).
Step 3: Choose one pair of consecutive angles to work with.
What pair are you using? <
and <
Measure each angle with a protractor. Write their measurements here:
What do you notice?
CONJECTURE: If two lines that are NOT parallel are cut by a transversal, then
consecutive angles are ____________________________________________.
Question: In the symbols of logic ( p  q ), how does this conjecture compare to the conjecture
about consecutive angles created by lines that ARE parallel and cut by a transversal?
Question: Do you think the other conjectures we made about alternate interior, alternate exterior,
and corresponding angles of PARALLEL lines cut by a transversal are TRUE if the lines are NOT
parallel?