Question

complete the two - column proof by dragging the statements into the correct answer space.
given: $angle s\cong\angle v$, and t is the midpoint of $overline{sv}$.
prove: $\triangle rts\cong\triangle utv$
image of two triangles $\triangle rts$ and $\triangle utv$ with t being the intersection point of their sides

statements	reasons
2. $overline{st}\congoverline{tv}$	2.
3. $angle rts\congangle vtu$	3.
4. $\triangle rts\cong\triangle utv$	4.

Explanation:

Step1: Identify Reason for Statement 1

The first statement is given in the problem, so the reason is "Given".

Step2: Identify Reason for Statement 2

Since T is the midpoint of $\overline{SV}$, by the definition of a midpoint, a midpoint divides a segment into two congruent segments. So $\overline{ST} \cong \overline{TV}$ because "Definition of Midpoint".

Step3: Identify Reason for Statement 3

$\angle RTS$ and $\angle VTU$ are vertical angles. Vertical angles are congruent, so the reason is "Vertical Angles Theorem".

Step4: Identify Reason for Statement 4

We have $\angle S \cong \angle V$ (given), $\overline{ST} \cong \overline{TV}$ (from midpoint), and $\angle RTS \cong \angle VTU$ (vertical angles). This is the ASA (Angle - Side - Angle) congruence criterion, so the reason is "ASA Congruence Postulate".

Answer:

1. Given
2. Definition of Midpoint
3. Vertical Angles Theorem
4. ASA Congruence Postulate