406 Chapter 16: Polygons So 6. 19 1eatibeloedsce es 1. Name each of the following polygons. If an adjective applies, use it also. a. b. d. c. e. f. go h. i. j. 2. If possible, sketch an example of each shape described. If not possible, explain why a. a trapezoid with at least one b. a hexagon with two sides perpendicular (make right angles, or angles of 90) a pentagon with two sides parallel d. a right angle C. regular quadrilateral (What is this shape usually called?) equiangular quadrilateral that is not equilateral (What is this shape usually called?) equilateral quadrilateral that is not equiangular (What is this shape usually called?) g. a parallelogram that has exactly h. a trapezoid that has equal-sized angles next to one of the parallel sides i. an isosceles right triangle k. an isosceles obtuse triangle m. a rhombus that is also a rectangle n. an isosceles triangle with all sides the same length 0. a kite with exactly one right angle p. an equilateral hexagon that is not a regular hexagon q. a regular pentagon that is not an equilateral pentagon 3. The reasonings below give incorrect conclusions. Explain why e. an f. an right angle one j. a scalene obtuse triangle I. an equilateral right triangle 7 a. "I don't get it. A hexagon has six sides, and each side has two endpoints, which are vertices of the hexagon. Six times two is twelve. Why doesn't a hexagon have twelve vertices?" b. "Hmm. An octagon has eight sides. It takes two sides to make an angle of the octagon. There are four two's in eight, so it seems that an octagon should have four angles, not eight!" 4.) Look around the room you are in (or a room in your imagination). What polygons and polygonal regions do you see? 8. 9 5. Many classrooms have sets of tangrams, cardboard or plastic pieces that can be fitted together to make a variety of shapes. The tangram pieces can be cut from a square region, as in the drawing shown at right. a. What shape is each of the seven tangram pieces? b. Using the segments in the drawing, find as many of each type of polygon as you can: isosceles right triangles; isosceles trapezoids; trapezoids that are not isosceles; parallelograms that are not rectangles. (Hint: Some may involve more than one tangram piece.) c. Let the entire square region be 1. Give the fractional value for each of the seven tangram pieces. d. Trace the tangram pieces, cut them out, and, without looking at the diagram, pu them together again to form a square. VI II IV VE III e. Tangrams are often used in classrooms to make different shapes. Can you use the pieces to make something-such as a cat?