For each figure or description below, make a conjecture (statement) and justify your conjecture with one or more reasons. Record your conjecture in your notes.

You may want to view some of the postulates, theorems, and definitions in the following links to help you.

- Theorems and Postulates for Geometry
- List of Definitions, Postulates, Theorems and Mathematical Properties

- What conjecture(s) can be made about the Rectangle MATH below?

- A certain polygon has the following characteristics.
- The polygon has four sides.
- Two consecutive angles of the polygon have measures of 65° and 115°.
- The diagonals of the polygon intersect at their midpoints.

Write as many conjectures about the polygon as you can, then describe the reasoning used to formulate your conjectures.

- A solid, four-inch cube of wood is coated with blue paint on all six sides. Then the cube is cut into smaller one-inch cubes. These new one-inch cubes will have either three blue sides, two blue sides, one blue side, or no blue sides. How many of each will there be?

Solution

See the **Resource** section for other websites with logic puzzles.

Click on the link below to play this matching game and see how well you know some geometry definitions and properties.