Question

Name the definition, postulate or theorem that justifies the statement.

If $\overline{\mathrm{RS}}\cong \overline{\mathrm{ST}}$, then S is the midpoint of $\overline{\mathrm{RT}}$.

Short answer

The theorem that justifies the statement is the midpoint theorem which states that the midpoint theorem states that if M is the midpoint of $\overline{\mathrm{AB}}$, then$\mathbf{AM}\mathbf{=}\frac{1}{2}\mathbf{AB}$ and$\mathbf{BM}\mathbf{=}\frac{1}{2}\mathbf{AB}$ and $\mathbf{AM}\cong \mathbf{BM}$.

Step-by-step solution

Step 1. Write the midpoint theorem.

The midpoint theorem states that if is the midpoint of $\overline{\mathrm{AB}}$, then $\mathbf{AM}\mathbf{=}\frac{1}{2}\mathbf{AB}$and $\mathbf{BM}\mathbf{=}\frac{1}{2}\mathbf{AB}$and $\mathbf{AM}\cong \mathbf{BM}$.

Step 2. Description of step.

It is being given that if $\overline{RS}\cong \overline{ST}$, therefore by using the midpoint theorem it can be said that is the midpoint of RT.

Step 3. Write the theorem that justifies the statement.

The theorem that justifies the statement is the midpoint theorem which states that the midpoint theorem states that if M is the midpoint of $\overline{AB}$, then $AM=\frac{1}{2}AB$and $BM=\frac{1}{2}AB$and $AM\cong BM$.