Download Geometry Session 6: Classifying Triangles Activity Sheet

Geometry Session 6: Classifying Triangles Activity Sheet – Classifying Triangles Try It Out: We saw in Session 5 that symmetry can be used for classifying designs. We will try this for triangles. The activity sheet for sorting triangles has several triangles to classify, but instead of looking at angles and sides, we will start with a question about symmetry – “Does the triangle have a line of symmetry?” Notice a flowchart has been started for you. Fill in the blanks as you sort and refine your sort. In addition to symmetry, we need some more information to classify triangles based as angles; we could use the idea that a right triangle can be circumscribed in a semicircle. The center of this circle is the midpoint of the hypotenuse. Consider the following questions: — How much does one endpoint of the longest side of a triangle need to be rotated about the midpoint of the longest side to make the other endpoint of the longest side its image? — When will the third vertex of the triangle be on the circle defining the rotation? — When will the third vertex of the triangle be in the exterior of the circle defining the rotation? — When will the third vertex of the triangle be in the interior of the circle defining the rotation? Reflect: • How does the symmetry sort compare to the traditional sort? • For the traditional sort, what tools would a student need to verify conditions? • For the transformation-­‐based sort, what tools would a student need to verify conditions? • Which set of tools relates more to geometric structure? Explain. B
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Is there a line of symmetry? No, it is scalene. From the midpoint of the longest side, can you circumscribe the 3 vertices? Yes, it is equilateral & equiangular. No. From the midpoint of the longest side, can you circumscribe the 3 vertices? No. Is the opposite vertex in the interior of the semicircle? No. Is the opposite vertex in the interior of the semicircle?