What Are Some Sample Answers to the Problems in "Discovering Geometry"?

# What Are Some Sample Answers to the Problems in "Discovering Geometry"?

One summary problem is, "What geometric shapes do each of these solids [a rectangular pyramid and a cylinder with a cylindrical hole going through it] contain?" A possible answer is, "The solids contain lines, segments, collinear and coplanar points, acute and right angles, triangles, a rectangle and concentric circles."

Another summary problem from "Discovering Geometry," published by Kendall Hunt, is, "Draw three line segments on a sheet of paper. Duplicate them to make a triangle, if possible." A sample answer to this problem is, "As long as the sum of any two lines is longer than the third, a triangle can be constructed. Constructing several triangles from the same three segments always yields the same triangle, although it may be a mirror image. So, provided that a triangle can be constructed, the triangle is determined."

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