I have drawn triangle ABC. Triangle ABC has 6 specific measurements: 3 specific side lengths and 3 specific angle measures. Your task is to recreate my hidden triangle.[br][br]Here is where it gets a little tricky - I am only going to give you [i][b]some[/b][/i] of those 6 specific measurements.[br][br]The purpose of the activities below is to determine what is the [i]least amount[/i] of information I can give you to construct a triangle that will be congruent to my original triangle.[br][br]To do this activity we are using a feature of GeoGebra called [u]sliders[/u]. The sliders will allow you to "slide" both angle measures and side lengths to set their size. Once you have moved the sliders to fit the given criteria, try and move other parts of the triangle.[br][br]After everyone has had a chance to make a triangle with the given criteria, we'll compare to see if the given information was enough to make everyone's triangles the [i][b]same as mine[/b][/i].[br]

[u][b]Attempt #1[/b]...one piece of given information[/u][br]For this first drawing I am going to give you one side length.[br][br][u]Draw triangle ABC with the given measure[/u]:[br][color=#ff0000]AB= 6.3[/color][br][br]Move the [color=#ff0000]red slider so that side AB has length 6.3[/color], then see if you can move any other parts of the triangle.

[u][b]Attempt #2[/b]...two pieces of given information[/u][br]For this next drawing I am going to give you one side length and one angle measure.[br][br][u]Draw triangle [i]ABC [/i]with the given measures[/u]:[br][color=#ff0000]AB = 6.3[/color][br][color=#38761d]angle CAB = 54 degrees[/color][br][br]Move the [color=#ff0000]red slider so that side [i]AB[/i] has length 6.3 [/color]and [color=#38761d]move the green slider so that angle [i]CAB[/i] is 54 degrees[/color]; then see if you can move any other parts of the triangle.

[u][b]Attempt #3[/b]...two pieces of given information[/u][br]For this next drawing I am going to give you two angle measures (really this is 3 angles, because when I give you two angles of a triangle, you know what the third angles is).[br][br][u]Draw triangle ABC with the given measures[/u]:[br][color=#38761d]angle CAB = 54 degrees[br][/color][color=#9900ff]angle CBA = 58 degrees[/color][br][br]Move the [color=#38761d]green slider so that angle [/color][i]CAB[/i][color=#38761d] is 54 degrees [/color]and move the [color=#9900ff]purple slider so that angle CBA is 58 degrees[/color]; then see if you can move any other parts of the triangle.

[u][b]Attempt #4[/b]...three pieces of given information[/u][br]For this next drawing I am going to give you two side lengths and the [i]included[/i] angle measure (an [i]included[/i] angle means that it is inbetween the 2 given sides) [br][br][u]Draw triangle ABCwith the given measures[/u]:[br][color=#ff0000]AB = 6.3[br][/color][color=#0000ff]BC = 5.5[/color][br][color=#9900ff]angle [i]CBA[/i] = 58 degrees[/color][br][br]Move the [color=#ff0000]red slider so that side [/color][i][color=#ff0000]AB[/color][/i][color=#ff0000] is 6.3[/color], move the [color=#0000ff]blue slider so that side BC is 5.5[/color], and move the [color=#9900ff]purple slider so that angle CBA is 58 degrees[/color]; then see if you can move any other parts of the triangle.

[u][b]Attempt #5[/b]...three pieces of given information[/u][br]For this next drawing I am going to give you three side lengths.[br][br][u]Draw triangle ABCwith the given measures[/u]:[br][color=#ff0000]AB = 6.3[br][/color][color=#0000ff]BC = 5.5[/color][br][color=#ff7700]AC = 5.76[/color][br][br]Move the [color=#ff0000]red slider so that side [/color][i][color=#ff0000]AB[/color][/i][color=#ff0000] is 6.3[/color], move the [color=#0000ff]blue slider so that side BC is 5.5[/color], and move the [color=#ff7700]orange slider so that side AC is 5.76[/color]; then see if you can move any other parts of the triangle.

[u][b]Attempt #6[/b]...three pieces of given information[/u][br]For this next drawing I am going to give you two angle measures and the [i]included[/i] side length (an [i]included[/i] side means it is inbetween the 2 given angles) [br][br][u]Draw triangle ABCwith the given measures[/u]:[br][color=#ff0000]AB = 6.3[/color][br][color=#38761d]angle CAB = 54 degrees[br][/color][color=#9900ff]angle CBA = 58 degrees[/color][br][br]Move the [color=#ff0000]red slider so that side [/color][color=#ff0000]AB[/color][color=#ff0000] is 6.3[/color], [color=#38761d]green slider so that angle CAB is 54 degrees [/color]and move the [color=#9900ff]purple slider so that angle CBA is 58 degrees[/color]; then see if you can move any other parts of the triangle.

[u][b]Attempt #7[/b]...three pieces of given information[/u][br]For this next drawing I am going to give you angle measures and the [i]non-included[/i] side length (a [i]non-included[/i] side means that it in NOT inbetween the 2 given angles) [br][br][u]Draw triangle ABC with the given measures[/u]:[br][color=#ff0000]AB = 6.3[/color][br][color=#9900ff]angle [/color][color=#9900ff]CBA[/color][color=#9900ff] = 58 degrees[br][/color][color=#ff00ff]angle ACB = 68 degrees[/color][br][br]Move the [color=#ff0000]red slider so that side AB is 6.3[/color], move the [color=#9900ff]purple slider so that angle CBA is 58 degrees[/color] and move the [color=#ff00ff]pink slider so that angle ACB is 68 degrees[/color]; then see if you can move any other parts of the triangle.

[u][b]Attempt #8[/b]...three pieces of given information[/u][br]For this next drawing I am going to give you side length and the [i]non-included[/i] angle measure (a [i]non-included[/i] angle means that it in NOT inbetween the 2 given sides) [br][br][u]Draw triangle ABC with the given measures[/u]:[br][color=#38761d]angle BAC[/color][color=#38761d] = 54 degrees[br][/color][color=#ff0000]AB = 6.3[/color][br][color=#0000ff]BC = 5.5[/color][br][br]Move the [color=#38761d]green slider so angle BAC is 54 degrees[/color] and move the [color=#ff0000]red slider so that side AB is 6.3[/color]. Then, [color=#0000ff]swivel side BC, which is set to 5.5[/color], until it matches up with the ray that comes from point A.

[u][b]Attempt #9[/b]...three pieces of given information[/u][br]For this last drawing we are working with a brand new trianlge. I am going to give you a more specific version of two side lengths and the [i]non-included[/i] angle measure. The angle needs to be 90 degrees.[br][br][u]Draw triangle ABCwith the given measures[/u]:[br][color=#6aa84f]angle CAB = 90 degrees[/color][br][color=#ff0000]AB = 5.5[br][/color][color=#0000ff]BC = 6.7[/color][br][br][br][color=#6aa84f]Angle CAB is set to 90 degrees[/color]. Move the [color=#ff0000]red slider so that side AB[/color][color=#ff0000] is 5.5[/color] and move the [color=#0000ff]blue slider so that side BC is 6[/color].[color=#0000ff]7[/color]; then see if you can move any other parts of the triangle.