Some tools
That ↑ is your task!
In order to examine the different cases for triangles, you will need tools for copying lengths and angles. One key feature is to use circles for copying lengths. Make sure you know how to do the tasks on this page before you continue to do the triangle cases
Make a triangle. If you have no other objects, the vertices of the triangle will be the points A, B and C. The sides of the triangle will be denoted AB=c, BC=a and AC=b
Copy length
Start with: A triangle ΔABC
Construct: A circle with radius c (c=AB). You should be able to move the circle around.
Construct: A segment with length c. You should be able to move the segment around.
The letters a, b and c are the names of the sides of the triangle. They are also so called variables, i.e. they have numerical values which you can use in mathematical expressions. The numerical value of the variable is, in this case, the length of the side.
Use the tool 
Segment with Given Length from Point. A pop up will show up where
you can enter a number.
Try making a few segments of various lengths. Enter c in the pop up window.
Right click on an object and choose Properties... Change the settings
of the labels from Name to Value.
In a similar way you can make a circle with radius c. Use the tool
Circle with Centre and Radius.
Copy angle
Start with: A triangle ΔABC
Construct: A segment and a ray having a common endpoint. The angle between the segment and the ray should have the same value as one of the angles of the triangle. Make sure that you know how to place the angle at any endpoint, clockwise or counter clockwise.
Use the tool 
Angle to measure the angle BAC. The angle will appear
in the Algebra View as α.
Enter a segment 
DE. Use the tool 
Angle with Given Size on the segment DE; enter α
in the pop up window.
You can use the tool
Angle with Given Size in two different ways.
If you start by clicking on a segment and then enter the angle, the angle will automatically appear at the first point of the segment.
If you first click on D, then on E, and then enter the angle; the angle DED' will be created; the angle will hence be placed at the point E.
Copy length to a segment on a given line
Start with: A triangle ΔABC and a line l through the points D and E
Construct: A segment having one endpoint at D. The segment should have the same length as the side AB and it should lie on the line l.
Like this ↓
by Malin Christersson under a Creative Commons Attribution-Noncommercial-Share Alike 2.5 Sweden License
