Question

1. given: \\(\overline{ma}\cong\overline{am}\\), m is the mid - point of \\(\overline{ab}). prove: \\(\overline{ma}\cong\overline{mb}). proof statements 1. \\(\overline{ma}\cong\overline{am}\\) 2. m is the mid - point of \\(\overline{ab}). 3. \\(\overline{am}\cong\overline{mb}\\) 4. \\(\overline{ma}\cong\overline{mb}\\) reasons 1. _ 2. _ 3. _ 4. _

Explanation:

Step1: State the given

Given that $M$ is the mid - point of $\overline{AB}$.

Step2: Recall mid - point definition

By the definition of a mid - point, if $M$ is the mid - point of $\overline{AB}$, then $\overline{AM}\cong\overline{MB}$.

Step3: Given congruence

We are also given that $\overline{MA}\cong\overline{AM}$.

Step4: Transitive property of congruence

Since $\overline{MA}\cong\overline{AM}$ and $\overline{AM}\cong\overline{MB}$, by the transitive property of congruence, $\overline{MA}\cong\overline{MB}$.

Answer:

1. Given
2. Definition of mid - point
3. Reflexive property of congruence
4. Transitive property of congruence