ANGLES OF A TRIANGLE

Introduction What makes a triangle a triangle?  What makes a triangle a unique triangle – one of a kind?  It’s all about sides and angles.  In this activity you will explore the angles of a triangle, noticing when a set of angles can determine a unique triangle, a set of triangles, or maybe only one triangle.  In the GeoGebra 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. The angle measurements colored in green are angles that you can change.  The angles colored in red are fixed angles that cannot be changed.  Step 1 Triangle ABC and its clone Triangle AABBCC have all green angles – all can be changed.  Use the MOVE tool to manipulate the clone Triangle AABBCC.   Can you construct another Triangle AABBCC that has the same angles as the original but is larger in size – is a similar triangle? Can you create triangles that are not similar to Triangle ABC?  Step 2  Use the MOVE GRAPHICS VIEW tool as necessary to move to the next pair of triangles. Triangle DEF and its clone Triangle DDEEFF have one of their three angles fixed at 52°.   Use the MOVE tool to manipulate the clone Triangle DDEEFF. Can you construct another Triangle AABBCC that has the same angles as the original but is larger in size – is a similar triangle? Can you create triangles that are not similar to Triangle DEF?  Step 3  Use the MOVE GRAPHICS VIEW tool as necessary to move to the next pair of triangles. Triangle XYZ and its clone Triangle XXYYZZ have two of their three angles fixed.  Use the MOVE tool to manipulate the clone Triangle DDEEFF.   Can you create triangles that are not similar to Triangle DEF?  Why is that? Hint: if you fix two angles in a triangle, what must happen to the third?   Conclusion 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.