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
To write a 2-column proof, we need to list the statements and the reasons for each step. Here's how you can prove the given statement using a 2-column proof:
Statement Reason
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1. QR || TU Given
2. QS = SR Definition of the midpoint
3. QSR is a triangle Definition of a triangle
4. TS = US Definition of the midpoint
5. TSU is a triangle Definition of a triangle
6. QS = TS Substitution (from statement 2 and 4)
7. SR = US Substitution (from statement 2 and 4)
8. QSR ≅ TSU Side-Angle-Side (SAS) congruence theorem
In this proof, we start with the given statement that QR is parallel to TU and S is the midpoint of QT. Then, we use definitions of midpoint and triangle to establish QS = SR and TS = US. Next, we justify that QSR and TSU are triangles based on their side lengths. Finally, we use the fact that QS = TS and SR = US to apply the SAS congruence theorem, concluding that QSR is congruent to TSU.