Write a 2-column proof for each of the following.
Given: QR|| TU , S is the midpoint of QT
Prove: /\QSR =~ /\TSU
/\ Is the triangle sign
Not on my drawing unless the length of QR = length of TU in addition to being parallel and TQRU is a rectangle
To write a two-column proof, you will need to list each statement or step on the left column and the corresponding reason or justification on the right column. Here is a two-column proof for the given statement:
Statement | Reason
--------------------------------------
1. QR || TU | Given
2. S is the midpoint of QT | Given
3. QS = SR, ST = SU | Definition of midpoint
4. /\QSR ≅ /\TSU | SAS (Side-Angle-Side) Congruence Theorem
Explanation:
1. The statement "QR || TU" is given initially, which states that line QR is parallel to line TU.
2. The statement "S is the midpoint of QT" is also given, which implies that point S divides line segment QT into two equal parts.
3. By the definition of midpoint, we know that QS is equal to SR and ST is equal to SU.
4. Using the SAS Congruence Theorem, we can conclude that /\QSR is congruent to /\TSU since they have two pairs of corresponding sides that are equal (QS = ST and SR = SU) and the included angles at S are congruent.
This completes the two-column proof for the statement.