Question

Give the Biconditional of the statement if possi 6le. If an angle is acute, then its measure is less than 90. If two angles are vertical then they are not congruent.

Answer 1

The biconditional for 'If an angle is acute, then its measure is less than 90 degrees' is 'An angle is acute if and only if its measure is less than 90 degrees'. For 'If two angles are vertical, then they are not congruent', the biconditional is inaccurate because vertical angles are always congruent; the correct statement would be 'Two angles are vertical if and only if they are congruent'.

Step-by-step explanation:

The biconditional of the statements given would be as follows:

• If an angle is acute, then its measure is less than 90 degrees becomes 'An angle is acute if and only if its measure is less than 90 degrees'.
• The second statement, If two angles are vertical, then they are not congruent, is actually not universally true because vertical angles are, by definition, always congruent. Therefore, a correct biconditional cannot be formed from this statement. Instead, the accurate statement would be 'Two angles are vertical if and only if they are congruent'.

In mathematics, conditional statements and their biconditionals are fundamental in understanding logical implications and equivalences. These concepts apply not only in geometry but also in algebra, calculus, and other branches. Biconditional statements are true when both the conditions occur together or neither occurs.