Exploring Properties of Parallel Lines
Name: Answer Key and Objectives
Goal: In this activity, you will use GeoGebra and your knowledge of parallel lines to investigate under
which conditions the definitions you have been given hold. Remember to use mathematical vocabulary
when answering questions (words like congruent, supplementary, complementary, etc)
Construction
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Construct line AB
Construct a line parallel to AB through a point C
Create the transversal BC which cuts through the two parallel lines
Create the following points:
 D on the line AB
 E on the line BC
 F on the line parallel to AB
 G on the line BC
 H on the line parallel to AB
o Your construction should look like Fig. 1
Fig. 1
Finishing the Construction & Questions

Find the measure of all angles in Fig. 1 and write them below.
There need to be 8 angles, <EBA, <ABC, <CBD, <DBE for line AD and <BCF, <FCG, <GCH, <HCB for line
FH
Students need to be able to use GeoGebra to measure angles and record their findings.
1. Do you notice any similarities or differences in the angle measurements? What are they?
Open-ended questions, they will receive points for identifying four of the angles are congruent and the
other four angles are also congruent. The two sets are supplementary.
Again, this is for the students to record their findings on paper rather than just continuously working.
2. Now grab the point C with the Move tool, and move the point around. Do the similarities you
pointed out in question 1 hold?
Yes.
Encourages students to check the conditions of their work and ensure they hold for all cases.
For questions 3-7, after answering each question, move points A, B, and C to see if the properties you
noticed hold.
3. <ABE and <FCB are corresponding angles. There are three more sets of corresponding angles in
the picture. Name them below.
<EBD and <BCH
<ABC and <FCG
<DBC and <HCG
4 sets of corresponding angles
Students need to unpack the definition and recognize the properties on their own. Giving students one
property and letting them explore the rest will help them to identify the angles in future
constructions.
4. <ABC and <BCH are alternate interior angles. There are three more sets of alternate interior
angles in the picture. Name them below.
<FCB and <CBD. These angles are congruent.
The same thought process as the last question, but identifying the property they share is important in
ensuring they use mathematical language.
5. Using what you know about alternate interior angles, find the alternate EXTERIOR angles of the
construction and write them below. Explain why you chose them.
<EBD and <FCG
<ABE and <GCH
exterior) of the construction.
because they are congruent angles on the outside (or
Has them put the property of alternate exterior angles in their own words, but they still need to be
using mathematical language.
6. <DBC and <HCB are same-side interior angles, find one more set of same-side interior angles.
What do you notice about these angles?
<ABC and <FCB
They are supplementary.
Same as questions 3-6, but focusing on supplementary angles rather than congruence.
Follow-up
7. If angle <ABC has a measure of 33 degrees, what is the measure of <BCH?
8. What angles are congruent to angle <ABE?
Non-Parallel Lines
The goal of this section will be to investigate if the properties we discovered in the last section still
hold.
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

Construct a line AB
Construct a line CD - not parallel to AB
Construct a transversal through points A and D
o Create points E, F, G, and H as in Fig. 2
Fig. 2

Find the measure of all angles in the construction and write them below.
There need to be 8 angles, <EBA, <ABC, <CBD, <DBE for line AD and <BCF, <FCG, <GCH, <HCB for
line FH
Students are to identify the differences between when the two lines cut by a transversal are
parallel or are not parallel. Parts a-d are to identify the specific properties that only hold for
parallel lines.
1. Do the following properties hold true for non-parallel lines:
a. Are the Corresponding Angles congruent?
No
b. Are the Alternate-Interior Angles congruent?
No
c. Are the Alternate-Exterior Angles congruent?
No
d. Are the Same-side Interior Angles supplementary?
No
Objectives
The main mathematical objectives of this activity are to have students explore the properties of
parallel lines. They are given a basic example of what the property is and are then asked to
discover more examples of the given property. This allows them to explore the properties on
their own and gives them more experience with GeoGebra, In addition, I had the students
explore properties on non-parallel lines, which tested the properties from the parallel lines in
the first section of the worksheet.
Exploring Properties of Parallel Lines
Name: ____________________________
Goal: In this activity, you will use GeoGebra and your knowledge of parallel lines to investigate under
which conditions the definitions you have been given hold. Remember to use mathematical vocabulary
when answering questions (words like congruent, supplementary, complementary, etc)
Construction




Construct line AB
Construct a line parallel to AB through a point C
Create the transversal BC which cuts through the two parallel lines
Create the following points:
 D on the line AB
 E on the line BC
 F on the line parallel to AB
 G on the line BC
 H on the line parallel to AB
o Your construction should look like Fig. 1
Fig. 1
Finishing the Construction & Questions

Find the measure of all angles in Fig. 1 and write them below.

Change the color of the angle measures so corresponding angles have the same color
3. Do you notice any similarities or differences in the angle measurements? What are they?
4. Now grab the point C with the Move tool, and move the point around. Do the similarities you
pointed out in question 1 hold?
For questions 3-7, after answering the question, move points A, B, and C to see if the properties you
noticed hold.
3. <ABE and <FCB are corresponding angles. Can you name the other corresponding angles in the
picture? How many sets of corresponding angles are there?
4. <ABC and <BCH are alternate interior angles. Can you name another pair of alternate interior
angles? What property do these angles share?
5. Using what you know about alternate interior angles, find the alternate EXTERIOR angles of the
construction and write them below. Explain why you chose them.
6. <DBC and <HCB are same-side interior angles, find another set of same-side interior angles. What
do you notice about these angles?
Non-Parallel Lines



Construct a line AB
Construct a line CD - not parallel to AB
Construct a transversal through points A and D
o Create points E, F, G, and H as in Fig. 2
Fig. 2

Find the measure of all angles in the construction and write them below.
1. Do the following properties hold true for non-parallel lines:
a. Are the Corresponding Angles congruent?
b. Are the Alternate-Interior Angles congruent?
c. Are the Alternate-Exterior Angles congruent?
d. Are the Same-side Interior Angles supplementary?