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 combines a conditional statement "if p then q" and its converse "if q then p" into "p if and only if q". Here, the original statement is "if M is the mid - point of $\overline{AB}$ then $\overline{AM}\cong\overline{MB}$", and its biconditional combines it with its converse.

Answer:

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