Answer:
∡A = ∡
being the base angle of an isosceles triangle of ΔABC
ΔAKE ≅ ΔCKP by

Explanation:
Given:
AB ≅ BC
AK ≅ KC
∡AKE ≅ ∡CKP
To prove:
ΔAKE ≅ ΔCKP
Solution:
Since AB ≅ BC
It means that
∡A = ∡C being the base angle of an isosceles triangle
In ΔAKE and ΔCKP
∡AKE ≅ ∡CKP Given Angle
AK ≅ KC Given Side
∡A = ∡C being the base angle of an isosceles triangle of ΔABC
Therefore,
ΔAKE ≅ ΔCKP by ASA axiom