Question

1. part b: select the word(s) in part a that made the statement become biconditional.

○ if and only if
○ not
○ if
○ then

1. part a: which statement is the contrapositive of:

if two angles are vertical angles, then they are not adjacent angles.
○ if two angles are not adjacent angles, then they are vertical angles.
○ if two angles are adjacent angles, then they are not vertical angles.
○ if two angles are not vertical angles, then they are adjacent angles.
○ two angles are vertical angles if, and only if, they are not adjacent angles.

Explanation:

Question 8

A biconditional statement is of the form "P if and only if Q", which means both "if P then Q" and "if Q then P" are true. Among the options, "If and only if" is the phrase that creates a biconditional statement. "not" negates a part, "if" starts a conditional, and "then" is part of a conditional but not for biconditional.

To find the contrapositive of a conditional statement "If P, then Q", we negate both P and Q and reverse their order, getting "If not Q, then not P". The original statement is "If two angles are vertical angles (P), then they are not adjacent angles (Q)". So not Q is "they are adjacent angles" and not P is "two angles are not vertical angles". So the contrapositive is "If two angles are adjacent angles, then they are not vertical angles".

Answer:

If and only if

Question 9