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

If two angles are adjacent, then they share a vertex.

Identify the hypothesis and conclusion of the conditional.

A figure is a parallelogram if it is a rectangle.

Find the length. Given below are the following coordinates:

A(-2.5,0)

B(1,0)

C(3.5,0)

D(5,0)

BC

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

Given: If Tommy makes cookies tonight, then Tommy must have an oven. Tommy has an oven.

Conjecture: Tommy made cookies tonight.

(F) The conjecture is valid, because if Tommy didn't have an oven then he didn't make cookies tonight.

(G) The conjecture is not valid, because if Tommy didn't have an oven then he didn't make cookies tonight.

(H) The conjecture is valid, because Tommy could have an oven but he could make something besides cookies tonight.

(J) The conjecture is not valid, because Tommy could have an oven but he could make something besides cookies tonight.

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

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

$\overrightarrow{F H}$ 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.

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

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

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) $X Y=V W$

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

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

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

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.