4. Suppose you decide to arrange tables in a square configuration with only a single row of tables on the ed square. As the arrangements increase in size, a square on the inside. Chairs will not be set in this space. ge of the square. Chairs will be set on only the outside of the there will be open space in the shape of a. Study the first two possible arrangements and then draw the next two in the sequence b. Generalize the number of chairs needed for n tables. Consider using an approach e the one shown in the section in which we determined how many chairs are needed for tables of a certain type. In this problem, there are corner tables and the interior tables are between the corner tables. Write an expression for the number of chairs and simplify it

Prove that if semicircles are constructed on each of the sides of a right triangle, then the area of the semicircle on the hypotenuse is equal to the sum of the areas of the semicircles on the two legs.

a Does the similarity relationship have a reflexive property for triangles and polygons in general? b Is there a symmetric property for the similarity of triangles and polygons? c Is there a transitive property for the similarity of triangles and polygons?

A carpenter lays out boards of lengths 8 ft, 8 ft, 4 ft, and 4 ft by placing them end to end. a If these are joined at the ends to form a quadrilateral that has the 8-ft pieces connected in over, what type of quadrilateral is formed? b If these are joined at the ends to form a quadrilateral that has the 4-ft and 8-ft pieces alternating, what type of quadrilateral is formed?