Question

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

not
if and only if
then
if

1. part a: which statement is a biconditional of:

if an angle is acute, then its measure is less than 90 degrees.
if an angle is not acute, then its measure is not less than 90 degrees.
an angle is acute if, and only if, its measure is less than 90 degrees.
if the measure of an angle is less than 90 degrees, then it is an acute angle.
an angle is acute if, and only if, its measure is not less than 90 degrees.

Explanation:

Question 6 (Part B)

To determine the word that makes a statement an inverse, recall that the inverse of a conditional statement "If \( p \), then \( q \)" is "If not \( p \), then not \( q \)". The word "not" is used to negate the hypothesis and conclusion, which is key in forming the inverse. "If and only if" is for biconditionals, "then" and "if" are part of the original conditional structure, not the inverse - forming word.

A biconditional statement combines a conditional statement and its converse, using "if and only if". The original statement is "If an angle is acute, then its measure is less than 90 degrees". Its converse is "If the measure of an angle is less than 90 degrees, then it is an acute angle". A biconditional combines these as "An angle is acute if, and only if, its measure is less than 90 degrees". The first option is the contrapositive, the third is the converse, and the fourth has an incorrect (negated) condition.

Answer:

not

Question 7 (Part A)