Download Exploring Complementary Angle relationships

Name:___________________________
Exploring Complementary Angle relationships
1. In Geogebra, right click on the background to turn off the axes and grid.
2. Go to the options tab, and change rounding to one decimal places, and labeling to all new
objects.
3. Go to the angle tool on the toolbar, and choose angle with given measure.
4. Click to place two points, and then choose 90° as your angle measure. Use rays to connect the
point that is your vertex to the points that are on your sides. You should have a right angle now.
What is the name of this right angle?__________________
5. Now, you will make another right angle. We want our two right angles to overlap, so choose as
your first point of the angle a place that is near one of the sides, but outside the first right angle.
Choose the same vertex point, and then 90° as the angle measure. Use rays to connect the
points and make an angle. It should look like the diagram below.
What is the name of the new angle you made?__________________________________
Name a pair of complementary angles in your diagram:____________________________
Name a different pair of complementary angles in your diagram:____________________
Notice, they both pairs share an angle! What angle is this?_________________________
6. Use the regular angle tool to find the measure of each of the three angles in your diagram.
Answer the following questions:
What is the measure of the shared angle?_______________________
Are both the angles complementary to this angle congruent?___________________
7. Now we will change the values of the angle. Grab the point that is not a prime point on the
interior of your overlapping rights angles. Keeping this point in the interior, slide it around and
find different values for the shared angle, and the angles complementary to these angles. Fill in
the table with these values.
Shared angle measure
Complementary angle 1
measure
Complementary angle 2
measure
What do you notice about these complementary angles and their relationship when they are
complimentary to the same angle?
Can you complete the following conditional statement?
If angles are complementary to the same angle, then _________________________________________.