Since MA is parallel to RY, the line segment AY is transversal to them and so angles MAY and RYA are congruent (alternate interior angles theorem).
AY is congruent to itself (reflexive property of congruence).
Angles M and R are congruent.
So if we pair up
- angles M and R
- angles MAY and RYA
- side AY with itself
we find that triangles MAY and RYA are congruent to one another (angle-angle-side triangles are congruent), and in turn corresponding sides are congruent to each other.
Therefore sides MY and RA are congruent.