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]some[/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 new 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]same as mine[/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 [i]ABC [/i]with the given measure[/u]:[br][color=#ff0000]Side [i]AB [/i]= 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]Side [i]AB [/i]= 6.3[/color][br][color=#38761d]angle [i]CAB[/i] = 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 [i]ABC [/i]with the given measures[/u]:[br][color=#38761d]angle [i]CAB[/i] = 54 degrees[br][/color][color=#9900ff]angle [i]CBA[/i] = 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]OK, 2 pieces of information didn't work, let's try three.[br]For this next drawing I am going to give you two side lengths and one angle measure (the [u]non-included[/u] angle - meaning it's [b]NOT[/b] the angle that is inbetween the 2 given sides).[br][br][u]Draw triangle [i]ABC [/i]with the given measures[/u]:[br][color=#38761d]angle [i]CAB[/i] = 54 degrees[br][/color][color=#ff0000]side [i]AB[/i] = 6.3[br][/color][color=#0000ff]side [i]BC[/i] = 5.5[/color][br][br]Move the [color=#38761d]green slider so that angle [i]CAB[/i] is 54 degrees[/color], move the [color=#ff0000]red slider so that side [i]AB[/i] has length 6.3[/color], and move[color=#0000ff] [u]point C[/u] until side [i]BC[/i] has length 5.5[/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]OK, those 3 pieces of information almost worked...we're getting closer, let's try a [i]different[/i] 3 pieces.[br]For this next drawing I am going to give you two side lengths and one angle measure (the [u]included[/u] angle - meaning it's the angle that is inbetween the 2 given sides).[br][br][u]Draw triangle [i]ABC [/i]with the given measures[/u]:[br][color=#9900ff]angle [i]ABC[/i] = 58 degrees[/color][color=#ff0000]side [i]AB[/i] = 6.3[br][/color][color=#0000ff]side [i]BC[/i] = 5.5[/color][br][br]Move the [color=#9900ff]purple slider so that angle [i]ABC[/i] is 58 degrees[/color], move the [color=#ff0000]red slider so that side [i]AB[/i] has length 6.3[/color], and move[color=#0000ff] blue slider until side [i]BC[/i] has length 5.5[/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]Let's try and see if three [i]different[/i] pieces of information will work.[br]For this next drawing I am going to give you three side lengths.[br][br][u]Draw triangle [i]ABC [/i]with the given measures[/u]:[br][color=#ff0000]side [i]AB[/i] = 6.3[br][/color][color=#0000ff]side [i]BC[/i] = 5.5[br][/color][color=#ff00ff]side [i]AC[/i] = 5.76[/color][br][br]Move the [color=#ff0000]red slider so that side [i]AB[/i] has length 6.3[/color], move the[color=#0000ff] blue slider so that side [i]BC[/i] has length 5.5[/color], and move the[color=#ff00ff] pink slider so that side [i]AC[/i] has length 5.5[/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]Let's try this again and see if three [i]different[/i] pieces of information will work.[br]For this next drawing I am going to give you three side lengths.[br][br][u]Draw triangle [i]ABC [/i]with the given measures[/u]:[br][color=#38761d]Angle [i]CAB[/i] = 54 degrees[br][/color][color=#9900ff]Angle [i]CBA[/i] = 58 degrees[/color][i][br][color=#ff0000]AB[/color][/i][color=#ff0000] = 6.3[br][/color][br][br]Move the [color=#ff0000]red slider so that side [i]AB[/i] has length 6.3[/color], move the [color=#38761d]green slider so that angle [i]CAB[/i] is 54 degrees[/color], and move the [color=#9900ff]purple slider so that angle [i]CBA[/i] is 58 degrees[/color]; then see if you can move any other parts of the triangle.