As you explore the characteristics of triangles, one idea to explore is "Which lengths make a Triangle?" Use the GeoGebra sketch to answer the five multiple choice questions. [br][br][color=#9900ff][b]Move[/b][/color] [b][color=#9900ff]the point on the slider[/color][/b] to change the length of the third side. [b][color=#00ff00]Move the green points[/color][/b] (B and C) until you are able to place both points labeled C on top of each other. If both points labeled C are on top of each other, the three lengths make a triangle.
You are asked to make a triangle with lengths of 5, 12, and 15. Is it possible? [br][i]Two of the three lengths are already given. So move the point on the slider to 15, then try to complete the triangle by placing one point C exactly on top of the other point C.[/i]
You are asked to make a triangle with lengths of 5, 12, and 8. Is it possible?
You are asked to make a triangle with lengths of 5, 12, and 6. Is it possible?
You are asked to make a triangle with lengths of 5, 12, and 11. Is it possible? [i].[/i]
You are asked to make a triangle with lengths of 5, 12, and 18. Is it possible?
Now you will further explore which lengths make triangles. In the GeoGebra sketch, you are given 3 lengths. Place the three lengths in the spreadsheet in order from [b][color=#0000ff]shortest to longest[/color][/b]. Also enter the sum of sides 1 and 2 into your spreadsheet.[br]Move the [b][color=#00ff00]green points[/color][/b] so they are exactly on top of each other. Then place either "Y" or "N" to indicate if a triangle is possible for the given lengths. [br]Click on [b][color=#9900ff]Next Problem[/color][/b] to explore other combinations. Create a table with 12 examples. Make sure you have examples of both situations (work or don't work).
For each set of lengths that make a triangle. how does the sum of [b][color=#a61c00]side1 + side 2[/color][/b] compare to the length of[b][color=#a61c00] side 3[/color][/b]?
If you are given three lengths in order from [color=#0000ff][b]shortest to longest[/b][/color], you will have a triangle when ...