Explanation:
1. T is the midpoint of QR, U is the midpoint of QS, and V is the midpoint of RS.
This is the information given in the problem statement.
2. TU, UV, and VT are midsegments
Midsegments connect midpoints of opposite sides. So TU, UV, and VT are midsegments.
3. TU = ½ RS, UV = ½ QR, and VT = ½ SQ
By Triangle Midsegment Theorem, a midsegment connecting the midpoints of two sides of a triangle is half the length of the third side.
4. TU/RS = 1/2, UV/QR = 1/2, VT/SQ = 1/2
Division property
5. TU/RS = UV/QR = VT/SQ
Transitive property
6. ΔQRS ~ ΔVUT
Since we've shown that the corresponding sides of these triangles are proportional, then by Converse of Similar Triangles Theorem, the triangles must be similar.