Use a protractor to draw a $70^{\circ}$ angle. Then use a compass and straightedge to bisect the angle. What do you think will be the measure of each angle formed? Use a protractor to support your answer.

Determine if the conjecture is valid by the Law of Detachment.

Given: If you want to go on a field trip, you must have a signed permission slip. Zola has a signed permission slip.

Conjecture: Zola wants to go on a field trip.

The class of 2004 holds a reunion each year. In 2005,87.5 percent of the 120 graduates attended. In 2006, 90 students went, and in 2007, 75 students went. About how many students do you predict will go to the reunion in 2010?

(A) 12

(B) 15

(C) 24

(D) 30

A, B, C, D, and E are collinear points. AE=34, BD=16, and AB=BC=CD. What is the length of $\overline{CE}$?

(F) 10

(G) 16

(H) 18

(J) 24

$\overrightarrow{F H}$ bisects $\angle E F G$. Use the Angle Addition Postulate to explain why m$\angle E F H=\frac{1}{2} \mathrm{~m} \angle E F G$.

Find a counterexample to show that the converse of each conditional is false.

If two angles are vertical angles, then they are congruent.

Which expression correctly states that $\overline{X Y}$ is congruent to $\overline{VW}$?

(A) $X Y \cong W W$

(B) $\overline{X Y} \cong \bar{W}$

(c) $\overline{X Y}=\bar{W}$

(D) $X Y=V W$

A student conjectures that if x is a prime number, then x+1 is not prime. Which of the following is a counterexample?

(F) x=11

(G) x=6

(H) x=3

(J) x=2

Find a counterexample to show that the converse of each conditional is false.

If x=-5, then x$^2=25$.

The measure of an obtuse angle is $(5 x+45)^{\circ}$. What is the largest value for $x$ ?

Can an obtuse angle be congruent to an acute angle? Why or why not?

Which of the following conjectures is false?

(A) If x is odd, then x+1 is even.

(B) The sum of two odd numbers is even.

(C) The difference of two even numbers is positive.

(D) If $x$ is positive, then $-x$ is negative.

C is the midpoint of $\overline{AD}$. B is the midpoint of $\overline{AC}$. BC=12. What is the length of $\overline{AD}$?

(F) 12

(G) 24

(H) 36

(J) 48

Q is between P and R . S is between Q and R, and R is between Q and T. PT=34, QR=8, and PQ=SQ=SR. What is the length of $\overline{RT}$?

(A) 9

(B) 10

(C) 18

(D) 22