91Ó°ÊÓ

If a pizza is cut into 16 congruent pieces, how many degrees are in each angle at the center of the pizza?

Write the first five terms of two different sequences in which 12 is the 3rd term.

Think of a situation you have observed in which inductive reasoning was used incorrectly. Write a paragraph or two describing what happened and explaining why you think it was an incorrect use of inductive reasoning.

Think of a situation in which you have used inductive reasoning. Write a paragraph describing what happened and explaining why you think you used inductive reasoning.

The sequence \(2,6,12,20,30,42, \ldots\) is called a rectangular number pattern because the terms can be visualized as rectangular arrangements of dots. What would be the 7th term in this sequence? What would be the 10 th term? The 25th term?

Look at the pattern in these pairs of equations. Decide if the conjecture is true. If it is not true, find a counterexample. $$\begin{array}{rll} 12^{2}=144 & \text { and } & 21^{2}=441 \\ 13^{2}=169 & \text { and } & 31^{2}=961 \\ 103^{2}=10609 & \text { and } & 301^{2}=90601 \\ 112^{2}=12544 & \text { and } & 211^{2}=44521 \end{array}$$ Conjecture: If two numbers have the same digits in reverse order, then the squares of those numbers will have identical digits, but in reverse order.

Study the pattern and make a conjecture by completing the fifth line. What would be the conjecture for the sixth line? What about for the tenth line? $$\begin{array}{rcc} 1 \cdot 1 & = & 1 \\ 11 \cdot 11 & = & 121 \\ 111 \cdot 111 & = & 12,321 \\ 1,111 \cdot 1,111 & = & 1,234,321 \\ 11,111 \cdot 11,111 & = & \underline{?} \end{array}$$

If a polygon has 24 sides, how many diagonals are there from each vertex? How many diagonals are there in all?

A midpoint divides a segment into two congruent segments. Point \(M\) divides segment \(\overline{A Y}\) into two congruent segments \(\overline{A M}\) and \(\overline{M Y} .\) What conclusion can you make? What type of reasoning did you use?

Use your ruler and protractor to draw a triangle with angles measuring \(40^{\circ}\) and \(60^{\circ}\) and a side between them with length \(9 \mathrm{cm}\). Explain your method. Can you draw a second triangle using the same instructions that is not congruent to the first?