Question

identify the biconditional for the following statement. if m is the midpoint of $overline{ab}$, then $overline{am}congoverline{mb}$. a. m is the midpoint of $overline{ab}$ only if $overline{am}congoverline{mb}$. b. $overline{am}congoverline{mb}$ only if m is the midpoint of $overline{ab}$. c. m is the midpoint of $overline{ab}$ if and only if $overline{am}congoverline{mb}$. d. if $overline{am}congoverline{mb}$, then m is the midpoint of $overline{ab}$.

Explanation:

A biconditional statement is of the form "p if and only if q", which combines a conditional statement "if p then q" and its converse "if q then p". Here, the original conditional is "If M is the mid - point of $\overline{AB}$, then $\overline{AM}\cong\overline{MB}$" and its converse is "If $\overline{AM}\cong\overline{MB}$, then M is the mid - point of $\overline{AB}$". The biconditional combines these two.

Answer:

C. $M$ is the midpoint of $\overline{AB}$ if and only if $\overline{AM}\cong\overline{MB}$