Write a 2-column proof
Given: RS=~TS, V is the midpoint of RT
Prove: /\RSV=~/\TSV
/\ is the triangle sign
To write a two-column proof, you need to list your statements (on the left column) and provide your reasons (on the right column) for each statement. Here is a two-column proof for the given information:
Statements | Reasons
-------------------------------------------------|------------------------
1. RS = TS | Given
2. V is the midpoint of RT | Given
3. RV = TV | Definition of midpoint
4. /\RSV ≅ /\TSV | Side-Angle-Side (SAS) congruence
Explanation:
1. The given statement tells us that the lengths of RS and TS are equal.
2. The given statement tells us that V is the midpoint of RT, which means RV and TV are equal in length.
3. The definition of the midpoint states that a midpoint divides a line segment into two equal parts. Therefore, RV = TV.
4. We can conclude that triangle RSV is congruent to triangle TSV using the Side-Angle-Side (SAS) congruence criterion. We have the following equalities:
a. RS = TS (given)
b. RV = TV (proved in statement 3)
c. Angle RSV = Angle TSV (by vertical angles)
Thus, /\RSV ≅ /\TSV.
This two-column proof shows the logical progression of statements and reasons that lead to the conclusion that /\RSV is congruent to /\TSV