Question

I need help with figuring out which converse makes QT parallel to MN

Answer 1

Since corresponding angles of similar triangles are congruent and triangles QRT and MRN are congruent, then:

$\angle RMN\cong\angle RQT.$

Now, notice that angles RMN and RQT are corresponding angles, then, using the corresponding angle theorem we get:

$QT\mleft\Vert MN\text{.}\mright?$

Answer: Second option.