Construct a triangle with vertices A,B,C. (Use the segment tool).
(To label points highlight the point and right click. Choose label point).
Measure the three angles of the triangle. (Highlight three points. Click Measure -> Angle) The middle point you click will be the
angle you have measured.
Calculate the sum of the angles. (Click to highlight all the angle measures. Go to Number ->Calculate. Click value to choose the
angle measure as a value and add them together).
What is the sum of your angles? __________________________________
Drag a vertex of the triangle and observe the angle sum. What happens the measures of the angles?
_______________________________________. What happens to the angle sum? _________________________________?
What can you conclude about the sum of the angles in any triangle?
____________________________________________________________________________________________________.
File-NEW SKETCH
Construct a triangle with vertices A,B,C. (Use the segment tool).
(To label points highlight the point and right click. Choose label point).
Construct Ray AC to extend the side AC. (Hold down the mouse on the Segment tool- fourth tool down- and drag right to choose
the Ray tool. Once you have the ray tool click point A and extend it to point C)
Construct point D on Ray AC outside the triangle. (Highlight Ray AC and choose Construct- Point on Ray- Right click and choose
label point to label the point D).
Measure the exterior angle BCD. (Highlight points B, C, D –make sure C is the center point- choose Measure- Angle).
Measure the non-adjacent interior angles ABC and CAB. (Use same steps above)
Drag parts of the triangle and look for a relationship between the measures of the remote interior angles and the exterior angle.
Calculate the sum of the non-adjacent interior angles. (Click to highlight the two appropriate angle measures. Go to Number >Calculate. Click value to choose the angle measure as a value and add them together).
How are the measures of the remote interior angles related to the measure of the exterior angle?
_______________________________________________________________________________________________________
____________________________________________________________________________________________
File- NEW SKETCH
Show a coordinate plane and turn on point snapping. (Graph- choose Show Grid, then choose Graph- Snap Points.)
Draw triangle A, B, C anywhere on the coordinate plane as long as there are integer coordinates. (Use segment tool-make sure
you have switched it back from Ray tool!)
Measure the coordinates of each vertex and record them here (Highlight the point choose -Measure- Coordinate)
A: ____________ B: ____________ C: ____________
Mark the y-axis as the “mirror” (Double click the y-axis- it should show a black box around it and then return to normal).
Reflect the triangle. (Highlight the entire triangle-points and segments- choose transform- Reflect.)
Label the points of the new triangle (Right click, label Point).
Measure the coordinates of each vertex and record them here (Highlight the point choose -Measure- Coordinate)
A’: ____________ B’: ____________ C’: ____________
Drag the vertices to different points on the grid and look for a relationship between the point’s coordinates and the coordinates
of the reflected image across the y-axis.
Describe the relationship you observe between the coordinates of the vertices of your original triangle and the coordinates of
their reflected images across the yaxis:_____________________________________________________________________________________________________
________________________________________________________________________________________________________.
Now: Move your triangle back to the original coordinates and mark the x-axis as the mirror (by
double clicking on it) and reflect your original triangle (follow directions from above).
Measure the coordinates (using directions from above) and record them here:
A’: ____________ B’: ____________ C’: ____________
Describe any relationship you observe between the coordinates of the original points and the
coordinates of their reflected images across the x-axis:
___________________________________________________________________________.
Now: Mark the origin as your center of transformation (Double click on the origin.)
Highlight all the points and segments of your original triangle.
Rotate the triangle 90 degrees counterclockwise. (Transform- Rotate- make sure it says 90 and click OK).
Record the points of your new triangle here:
A’: ____________ B’: ____________ C’: ____________
Will the triangle ever rotate back to its original position, if so, how?
_______________________________________________________________________________________________________.
If you continue to rotate 90 degrees counterclockwise, how many additional transformations would it take to get it back to the
original position? _________________________________ (Try it!)