ai) Since △ABC is congruent to △CDE,
∠ABC = ∠CDE = 38°

ii)  ∠CED = 180° – 114° – 38°
= 28°

iii) ∠ACB = ∠CED = 28°

iv) BC = DE = 27 cm

v) CE = AC = 18 cm
BE = BC – CE
= 27 – 18
= 9 cm

b) They are parallel

Explanation:

∠ACB = ∠CED = 28°
∠ ACD = ∠ACB + ∠DCE
= 114° + 28°
= 142°

Since ∠CDE = 38°, ∠CDE + ∠ACD = 180°

Therefore, lines AC and ED are parallel (interior angles between parallel lines add up to 180°)