Section 1
If-Then Statements; Converses
Write the hypothesis and the conclusion of each conditional.If $3 x-7=32,$ then $x=13$
Write the hypothesis and the conclusion of each conditional.I can't sleep if I'm not tired.
Write the hypothesis and the conclusion of each conditional.I'll try if you will.
Write the hypothesis and the conclusion of each conditional.If $m \angle 1=90,$ then $\angle 1$ is a right angle.
Write the hypothesis and the conclusion of each conditional.$a+b=a$ implies $b=0$.
Write the hypothesis and the conclusion of each conditional.$x=-5$ only if $x^{2}=25$.
Rewrite each pair of conditionals as a biconditional.If $B$ is between $A$ and $C$, then $A B+B C=A C$. If $A B+B C=A C,$ then $B$ is between $A$ and $C$.
Rewrite each pair of conditionals as a biconditional.If $m \angle A O C=180,$ then $\angle A O C$ is a straight angle. If $\angle A O C$ is a straight angle, then $m \angle A O C=180$.
Write each biconditional as two conditionals that are converses of each other.Points are collinear if and only if they all lie in one line.
Write each biconditional as two conditionals that are converses of each other.Points lie in one plane if and only if they are coplanar.
Provide a counterexample to show that each statement is false. You may use words or a diagram.If $a b<0,$ then $a<0$.
Provide a counterexample to show that each statement is false. You may use words or a diagram.If $n^{2}=5 n,$ then $n=5$.
Provide a counterexample to show that each statement is false. You may use words or a diagram.If point $G$ is on $\overrightarrow{A B},$ then $G$ is on $\overrightarrow{B A}$.
Provide a counterexample to show that each statement is false. You may use words or a diagram.If $x y>5 y,$ then $x>5$.
Provide a counterexample to show that each statement is false. You may use words or a diagram.If a four-sided figure has four right angles, then it has four congruent sides.
Provide a counterexample to show that each statement is false. You may use words or a diagram.If a four-sided figure has four congruent sides, then it has four right angles.
Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.If $x=-6,$ then $|x|=6$.
Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.If $x^{2}=4,$ then $x=-2$.
Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.If $b>4,$ then $5 b>20$.
Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.If $m \angle T=40,$ then $\angle T$ is not obtuse.
Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.If Pam lives in Chicago, then she lives in Illinois.
Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.If $\angle A \cong \angle B,$ then $m \angle A=m \angle B$
Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.$a^{2}>9$ if $a>3$.
Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.$x=1$ only if $x^{2}=x$.
Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.$n>5$ only if $n>7$.
Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.$a b=0$ implies that $a=0$ or $b=0$.
Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.If points $D, E,$ and $F$ are collinear, then $D E+E F=D F$.
Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.$P$ is the midpoint of $\overline{G H}$ implies that $G H=2 P G$
Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.Write a definition of congruent angles as a biconditional.
Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.Write a definition of a right angle as a biconditional.
Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.What can you conclude if the following sentences are all true?(1) If $p,$ then $q$ ( 2)$p$(3) If $q,$ then not $r$(4) $s$ or $r$