VTMO 2019 — Grade 7 — final Question 5

$a$)Equal segments $AB , CD$ intersect at $K$ with $AC$ parallel to $BD$. Prove $KA = KC$. $b ) ABC$ is isosceles at $A , BD$ bisects $B , D$ on $AC$, and altitude $AH = \frac{BD}{2}$. Find $A$.