Download Parallel Lines and Transversals Investigation

NAME _____________________________PD____ DATE____________
INVESTIGATION: PROPERTIES OF PARALLEL LINES
STEP 1: Go to the following website:
http://www.mathwarehouse.com/geometry/angle/interactive-transveral-angles.php
STEP 2: Click on the DIRECTIONS button located under the “Angles of Parallel Lines
and A Transversal” heading.
STEP 3: Carefully READ the directions for how to move the lines, then click the
DIRECTIONS button again to close the box.
STEP 4: Experiment with moving the parallel lines and the transversal. Roll the mouse over
different angles and observe how the measurements light up.
PART 1: CORRESPONDING ANGLES
Click on the button labeled CORRESPONDING ANGLES located on the right hand side
of the page. Corresponding angles will be color-coded.
A. Locate 2 pairs of corresponding angles and record their measurements:
ANGLE
MEASUREMENT
1a.
1b.
2a.
2b.
Sketch the BOTH Corresponding Angles below. Accurately, label the angles WITH the
appropriate degrees
NAME _____________________________PD____ DATE____________
B. MOVE the parallel lines and the transversal. Locate 2 pairs of corresponding angles
and record their measurements:
ANGLE
MEASUREMENT
3a.
3b.
4a.
4b.
Sketch TWO MORE Corresponding Angles with their correct labels and degrees
What do you notice about the corresponding angles?
Compare your results with your partner(s).
Make a conjecture based on the information you collected.
When parallel lines are cut by a transversal, corresponding angles formed
are_________________________.
(CORRESPONDING ANGLES CONJECTURE)
NAME _____________________________PD____ DATE____________
PART 2: ALTERNATE INTERIOR ANGLES
Click on the button labeled ALTERNATE INTERIOR ANGLES located on the right hand
side of the page. Alternate interior angles will be color-coded.
A. Locate 2 pairs of alternate interior angles and record their measurements:
ANGLE
MEASUREMENT
1a.
1b.
2a.
2b.
Sketch a TWO pairs of Alternate Interior Angles below. Accurately, label the angles
WITH the appropriate degrees
NAME _____________________________PD____ DATE____________
B. MOVE the parallel lines and the transversal. Locate 2 pairs of alternate interior
angles and record their measurements:
ANGLE
MEASUREMENT
3a.
3b.
4a.
4b.
Sketch TWO more pairs of Alternate Interior Angles below. Accurately, label the
angles WITH the appropriate degrees
What do you notice about the alternate interior angles?
Compare your results with your partner(s).
Make a conjecture based on the information you collected.
When parallel lines are cut by a transversal, alternate interior angles formed
are______________________________.
(ALTERNATE INTERIOR ANGLES CONJECTURE)
NAME _____________________________PD____ DATE____________
PART 3: ALTERNATE EXTERIOR ANGLES
Click on the button labeled ALTERNATE EXTERIOR ANGLES located on the right hand
side of the page. Alternate exterior angles will be color-coded.
A. Locate 2 pairs of alternate exterior angles and record their measurements:
ANGLE
MEASUREMENT
1a.
1b.
2a.
2b.
Sketch TWO pairs of Alternate EXTERIOR Angles below. Accurately, label the angles
WITH the appropriate degrees
B.
NAME _____________________________PD____ DATE____________
MOVE the parallel lines and the transversal. Locate 2 pairs of alternate exterior
angles and record their measurements:
ANGLE
MEASUREMENT
3a.
3b.
4a.
4b.
Sketch TWO more pairs of Alternate EXTERIOR Angles below. Accurately, label the
angles WITH the appropriate degrees
What do you notice about the alternate exterior angles?
Compare your results with your partner(s). Make a conjecture based on the information
you collected.
When parallel lines are cut by a transversal, alternate exterior angles formed
are______________________________.
(ALTERNATE EXTERIOR ANGLES CONJECTURE)
NAME _____________________________PD____ DATE____________
PART 4: SAME-SIDE INTERIOR ANGLES (A.K.A CONSECUTIVE)
A. Locate 2 pairs of same-side interior angles (A.K.A CONSECUTIVE) and record
their measurements:
ANGLE
1a.
1b.
2a.
2b.
MEASUREMENT
NAME _____________________________PD____ DATE____________
B. MOVE the parallel lines and the transversal. Locate 2 pairs of same-side interior
angles and record their measurements:
ANGLE
MEASUREMENT
3a.
3b.
4a.
4b.
Sketch 2 examples of consecutive angles. Be sure to label the angles and include the
degrees,
What do you notice about the same-side interior angles?
Compare your results with your partner(s). Make a conjecture based on the information
you collected.
When parallel lines are cut by a transversal, same-side interior angles
(CONSECUTIVE) formed are______________________________.
(SAME-SIDE INTERIOR ANGLES CONJECTURE)
NAME _____________________________PD____ DATE____________
SUMMARY
Corresponding Angles Conjecture: If two parallel lines are cut by a transversal, then
the corresponding angles are _____________________.
Conversely, If two lines are cut by a transversal form pairs of congruent corresponding
angles, then the lines are parallel
Alternate Interior Angles Conjecture: If two parallel lines are cut by a transversal,
then the alternate interior angles are ___________________.
Conversely,
__________________________________________________________________
_________________________________________________________________.
Alternate Exterior Angles Conjecture: If two parallel lines are cut by a transversal,
then the alternate exterior angles are __________________.
Conversely,
__________________________________________________________________
__________________________________________________________________
Same-Side Interior Angles (CONSECUTIVE ANGLES) Conjecture: If two parallel
lines are cut by a transversal, then the same-side interior angles are ______________.
Conversely,
__________________________________________________________________
__________________________________________________________________
NAME _____________________________PD____ DATE____________
FINAL CHECKS FOR UNDERSTANDING
1
5
9
13
2
3
6
10
14
7
11
15
c
4
a
8
12
16
b
d
Given a // b, name all angles which are congruent to 4. ____________________
Given c // d, name all angles which are congruent to 16.____________________
Given a // b and c // d, name all angles which are congruent to 1._____________
2
120
1
a. m ∠ 1 = ______
REASON:
______________
b. m ∠ 2 = _____
REASON:
______________
a. m ∠ 1 = ______
REASON:
______________
b. m ∠ 2 = _____
REASON:
______________
a. m ∠ 1 = ______
REASON:
______________
b. m ∠ 2 = _____
REASON:
______________
ALGEBRA: Now, try this one. Solve for “x” and the angle:
(x + 10)º
115º