Controlling Angles with Sliders: Ex. 14
- Author:
- Tim Brzezinski
- Topic:
- Angles, Mathematics
DIRECTIONS:
1) Construct a segment .
2) Select the SLIDER 
tool. Select ANGLE. Set Min = . Set Max = . Set Increment = .
Hit OK. Slider should be named .
3) Select the ANGLE WITH GIVEN SIZE 
tool.
Select point B. Then select point A (vertex of soon-to-appear angle).
Then, where it says , delete this and replace with (see menu off to right).
Select COUNTERCLOCKWISE. If you do this correctly, you should see a new point B' so that
.
4) Construct a ray with endpoint B that passes through B'.
5 )Select the ANGLE WITH GIVEN SIZE tool. Select point A. Then select point B.
Then, where it says , delete this and replace with (see menu off to right).
Select CLOCKWISE. You should see a new point A' so that .
More directions appear below the applet.
tool. Select ANGLE. Set Min = . Set Max = . Set Increment = .
Hit OK. Slider should be named .
3) Select the ANGLE WITH GIVEN SIZE tool.
Select point B. Then select point A (vertex of soon-to-appear angle).
Then, where it says , delete this and replace with (see menu off to right).
Select COUNTERCLOCKWISE. If you do this correctly, you should see a new point B' so that
.
4) Construct a ray with endpoint B that passes through B'.
5 )Select the ANGLE WITH GIVEN SIZE tool. Select point A. Then select point B.
Then, where it says , delete this and replace with (see menu off to right).
Select CLOCKWISE. You should see a new point A' so that .
More directions appear below the applet. 6) Construct a ray with endpoint A that passes through A'.
7) Plot the point of intersection of the 2 rays you've just constructed in steps (4) & (6).
8) Go to the algebra view (left). Hide the 2 rays, the original segment , and the points A' and B'.
9) Use the POLYGON tool with vertices A, B, and the point of intersection of the 2 rays you constructed in step (7).
10)
Display the length of all sides of this triangle. Move the slider around. What do you notice? What can we conclude about a triangle with 2 congruent angles?
11)
What happens if we set ?
When you're done (or if you're unsure of something), feel free to check by watching the quick silent screencast below.