[left][color=#000000][b]Introduction[br][/b]What makes a triangle a triangle?  [br]What makes a triangle a unique triangle – one of a kind? [br]It’s all about sides and angles.  [br][br]In this activity you will explore the [b][i]angles of a triangle[/i][/b], noticing when a set of angles can determine a unique triangle, a set of triangles, or maybe only one triangle. [br][br]In the [i]GeoGebra[/i] workspace, there are three pairs of triangles:  Triangle ABC, Triangle DEF, and Triangle XYZ.   Next to each is a “clone” with which you can experiment.  Don't alter the triangles on the left, the originals, only the clones.[br][br]The angle measurements colored in green are angles that you can change.  The angles colored in red are fixed angles that cannot be changed. [br][br][b]Step 1[br][/b]Triangle ABC and its clone Triangle AABBCC have all green angles – all can be changed. [br]Use the MOVE tool to manipulate the clone Triangle AABBCC.  [br]Can you construct another Triangle AABBCC that has the same angles as the original but is larger in size – is a [i][b]similar triangle[/b][/i]?[br]Can you create triangles that are not [b][i]similar[/i] [/b]to Triangle ABC? [br][br][b]Step 2[/b]  [br]Use the MOVE GRAPHICS VIEW tool [icon]/images/ggb/toolbar/mode_translateview.png[/icon]as necessary to move to the next pair of triangles.[br]Triangle DEF and its clone Triangle DDEEFF have one of their three angles fixed at 52°.  [br]Use the MOVE tool to manipulate the clone Triangle DDEEFF. [br]Can you construct another Triangle AABBCC that has the same angles as the original but is larger in size – is a [i][b]similar triangle[/b][/i]? [br]Can you create triangles that are not [i]similar[/i] to Triangle DEF? [br][br][b]Step 3[/b][b] [/b] [br]Use the MOVE GRAPHICS VIEW tool [icon]https://tube.geogebra.org/images/ggb/toolbar/mode_translateview.png[/icon]as necessary to move to the next pair of triangles.[br]Triangle XYZ and its clone Triangle XXYYZZ have two of their three angles fixed. [br]Use the MOVE tool to manipulate the clone Triangle DDEEFF.  [br]Can you create triangles that are not [i]similar[/i] to Triangle DEF?  [br]Why is that? Hint: if you fix two angles in a [/color]triangle, what must happen to the third?  [br][br][color=#000000][b]Conclusion[br][/b]Summarize what you have learned about the angles of triangles and whether or not, given a set of angles, you can create a completely different triangle or only a similar triangle. [/color][/left]