Replacement activity for Tuesday, 7 April

There are a few reasons why our activity for today, 6.14 has been bothering me.  Without wasting all your time elaborating, the simple ones are 1. I doubt many of you have compasses, and 2. I usually give a good amount of guidance during this activity.  

So, let's try this for today:

1. Please go here:

https://www.euclidea.xyz

Select "play now"

Select "alpha"

*Note:  you may want to make this full screen so that you can see the tools on the bottom of the screen*  *If can't see the tools, the two most important are circle and line.  If you ever want to make a circle, press the circle on your keyboard (the letter 'O').  If you ever want to make a line, press the capital 'i' on your keyboard, that looks like a line.*

Try to complete the following:

Tutorial:  Line Tool
Tutorial:  Circle Tool
Tutorial:  Point Tool (these just give you practice using the software)
Equilateral Triangle
and then as many as you can starting with
1. Angle of 60 degrees
2. Perpendicular bisector
Tutorial:  Perpendicular Bisector
3. Midpoint
4. Circle in Square
and so on ...

Spend no more than 30 minutes doing this.  (You might even want to move on when you have 45 minutes remaining.)

2. Look back to activity 7.18 that we did a while ago (on 5 March, for those who date your notes)

If you start with a side-angle-side configuration, as in 7.18 I a, what did you do to finish the triangle?  Because of this, at most how many triangles can be made from a given side-angle-side configuration?  (This was 7.18 I c)

If you start with an angle-side-angle configuration, as in 7.18 II a, what did you do to finish the triangle?  Because of this, at most how many triangles can be made from a given angle-side-angle configuration?  (This was 7.18 II c)

3. Now look at activity 6.5 that we did on the very same day.  Look at your work for 6.5 I Triangles (a).  Compare it to this compass and straightedge construction:

https://www.mathsisfun.com/geometry/construct-tricopy.html

If you start with three given side lengths, at most how many different (meaning non-congruent) triangles can you make?  Be careful to explain why this works.  What choices did they make in the short video?  There are many choices, but why do they all produce the same triangles?

4. For activity 6.5 I Triangles (e), how many different triangles could you make?   What does this say  about angle-angle-angle configurations?

5. Next look back at activity 7.18 II (e).  Based on that one example, at most how many triangles can be made from a given angle-angle-side configuration?

6. Lastly look at activity 7.18 I (e).  Consider in particular starting with the 60 degree angle, then the 4 cm side, then the 6 cm side.  How many triangles can you make with this information?  

This configuration is the trickiest.  To see this, try to start with a 30 degree angle, then a 6 cm side, and finally a 4 cm side.  How many triangles can you make now?   

This is better  than AAA was, but not as good as the others.  Sometimes there can be two triangles.  Sometimes this is a  good test and sometimes there are problems.

2-6 are the subject of your final geometry weekly question.  So, naturally make as much sense of this as you can.  

If you happen to have extra time, because you reviewed 7.18 and 6.5 so well ... more playtime with constructions!