91Ó°ÊÓ

Name or state the postulate, definition, or theorem that justifies each statement about the diagram.

$AE+EC=AC$.

$n^2+n+11$Draw several diagrams to help you decide whether each statement is true or false. If it is true, draw and label a diagram you could use in a proof. List, in terms of the diagram, what is given and what is to be proved. Do not write proof.

a. Substitute each of the integers from 1 to 9 for n in the expression $n^2+n+11$.

b. Using inductive reasoning, guess what kind of number you will get when you substitute any positive integer for n in the expression $n^2+n+11$.

c. Test your guess by substituting 10 and 11 for n.

Given: The measure of each interior angle of a regular n-gon is x times that of an exterior angle.

1. Express x in terms of n.
2. For what values of n will x be an integer?

Plot each point on graph paper.

$E(-3,1)$.

Exercises 23 – 29 refer to the diagram in Step 2 of Exercise 22

Suppose the top and bottom of the box lie in parallel lines. Explain how theorem 3.1 can be used to prove $\stackrel{¯}{CD}\text{ }âˆ\yen \text{ }\stackrel{¯}{IJ}$.

Find the values of x and y that make the lines shown in red parallel.

Find the values of x and y.

Name or state the postulate, definition, or theorem that justifies each statement about the diagram.

$m∠1+m∠2=m∠ABC$

Complete the table for convex polygons.

Plot each point on graph paper.

$F(-2,-1)$.