Question

proof: complete the flow proof by dragging the statements and reasons. given: $overline{rs} cong overline{ts}$, $v$ is the midpoint of $overline{rt}$. prove: $\triangle rsv cong \triangle tsv$
proof:
flow proof diagram and image of triangle with points r, v, t, s
statements and reasons boxes: reflective prop., sss, def. of midpoint, $overline{rs} cong overline{ts}$, $overline{rv} cong overline{tv}$, $overline{sv} cong overline{sv}$
need help?

Explanation:

Step1: Identify Given Information

We know \( \overline{RS} \cong \overline{TS} \) (given) and \( V \) is the midpoint of \( \overline{RT} \), so \( \overline{RV} \cong \overline{TV} \) (by definition of midpoint). Also, \( \overline{SV} \cong \overline{SV} \) (reflexive property of congruence).

Step2: Use SSS Congruence Criterion

For \( \triangle RSV \) and \( \triangle TSV \):

• \( \overline{RS} \cong \overline{TS} \) (given)
• \( \overline{RV} \cong \overline{TV} \) (midpoint definition)
• \( \overline{SV} \cong \overline{SV} \) (reflexive property)

By SSS (Side - Side - Side) congruence postulate, \( \triangle RSV \cong \triangle TSV \).

Now, filling the flow proof:

• The top blue box (statement) should be \( \overline{RS} \cong \overline{TS} \) (given).
• The box below it (reason) can be related to the given, but the key is the congruence. The box from "V is the midpoint" leads to \( \overline{RV} \cong \overline{TV} \) (by Def. of midpoint). The reflexive property gives \( \overline{SV} \cong \overline{SV} \), and then SSS is the reason for \( \triangle RSV \cong \triangle TSV \).

Answer:

To complete the flow proof:

• The statement for the top blue box: \( \boldsymbol{\overline{RS} \cong \overline{TS}} \) (Given)
• The statement from "V is the midpoint of \( \overline{RT} \)" leads to: \( \boldsymbol{\overline{RV} \cong \overline{TV}} \) (Def. of midpoint)
• The reflexive property statement: \( \boldsymbol{\overline{SV} \cong \overline{SV}} \)
• The reason for \( \triangle RSV \cong \triangle TSV \): \( \boldsymbol{SSS} \) (Side - Side - Side Congruence Postulate)

(When dragging the statements and reasons: Drag \( \overline{RS} \cong \overline{TS} \) to the top blue box, \( \overline{RV} \cong \overline{TV} \) to the box below "V is the midpoint", \( \overline{SV} \cong \overline{SV} \) (using reflexive prop.) to the appropriate box, and \( SSS \) as the reason for the congruence of the triangles.)