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Geometer’s Sketchpad Activities
Exploring Geometry
Intersecting Lines & Their Angles
When two lines intersect they form four angles. The point of intersection of the lines is the vertex of all four
angles. In this activity, you’ll investigate relationships between pairs of these angles.
Sketch and Investigate
C
B
 Construct line AB and line CD so that they intersect.
 Construct a point at their intersection.
 Label all of the points.
E
D
A
 Use GSP to measure all four angles.
To measure an angle,
select three points. Make
sure that you select the
point you want to be the
vertex in the middle of your
selection. Then in
MEASURE menu, choose
ANGLE.
 Drag one of the points and look for a relationship among the angle measures.
Make sure to keep point E between points A and B and between points C and D.
Points to Ponder
In your sketch, DEB and CEA are a pair of Vertical Angles.
In your sketch, CEB and BED are a pair of Linear Angles, because their
external (outside) rays are opposite rays and form a line.
 Name another pair of Vertical Angles _____________________ .
Write a conjecture, about them:
 Name all of the other pairs of Linear Angles _________________________.
Write a conjecture, about them:
Things to Do . . .
1. Drag a point in your sketch until all the angles in a linear pair are congruent (the
same measure). Describe all four angles.
2. Make a pair of Hide/Show buttons for 3 of the angles. To do this…
 Select the measurements of the three angles by holding the “shift” button down
and “clicking” on each measurement with your selection tool. Then,
 Choose the “ACTION BUTTON: HIDE/SHOW” item from “EDIT” menu.
840970572, Created by S. Middleton
1
revised: 05/03/17
3. Double–Click on the “Hide” Button. It should hide the three measurements you
selected.
4. With these measurements hidden, select one of the points of your sketch and
drag it until the visible angle measurement is 63°. Make a guess of what the
measures of the three “hidden”angles are. Write your guess down here: _______
________
_______
Then, double-click on the “Show” button to reveal the measures. Check your guess
to see if it is correct.
Test yourself a few more times, by using the “hide” button to hide the angle
measures, drag the point to change the measure of the visible angle, guess the
remaining measurements, and reveal the other three to check your guesses.
Going Further & Deeper . . .
Use sketchpad to do the following investigations:
Suppose you had Three (3) lines that all intersected at one point to form six
angles.
 How many angles would you need to know in order to find the other measures?
 Describe any situations in which all the angles are congruent.
Suppose you had Four (4) lines that all intersected at one point to form eight
angles.
 How many angles would you need to know in order to find the other measures?
 Describe any situations in which all the angles are congruent.
Now, using the previous two conditions, make a generalization about the number of
lines (n) that intersect and the number of angles (2n) that form.
840970572, Created by S. Middleton
2
revised: 05/03/17