By Frederick S. Woods

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Do the same observations hold? c. Draw a scalene triangle. Locate the midpoints of two of the sides. Then draw a line segment connecting the midpoints. Compare the segment with the third side of the triangle. Do the observations you made in part (a) also apply in this case? Now connect the midpoints of a different pair of sides. Do the same observations hold? 44. Two lines are perpendicular if they intersect to form right angles. Tell whether the statement below is true or false. Justify your answer.

2 95º 50º 1 3 A. 1. What are the measures of the interior angles of the triangle? 2. What is the measure of angle 1? 3. What are the measures of angle 2 and angle 3? B. Suppose the skateboarder skates once around the park counterclockwise, turning each corner exactly once. What is the sum of the angles through which she turns? C. 1. Draw another triangle and mark the exterior angles going in one direction around the triangle. 2. Measure the exterior angles and find the sum. 3. Compare the exterior angle sum of your triangle to the sum you found for the triangle in Question B.

However, there are some mathematical properties of hexagons that may offer explanations. Below is a tiling of regular hexagons. Notice that three angles fit together exactly around any point in the tiling. Why do these regular hexagons fit together so neatly? 3, you experimented to find which regular polygons could tile a surface. What are the properties of these shapes that allow them to fit together so neatly around a point? 3 Angles in Tilings A. 3, you explored tilings made from a single type of regular polygon.

### A course in mathematics,: For students of engineering and applied science, by Frederick S. Woods

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