Answer: the prove is mentioned below.
Step-by-step explanation:
Here, Segment BK (K∈ AC ) is the angle bisector of ∠B in ΔABC. Point M is chosen on the side BC so that MK ≅ MB
We have to prove that: KM ∥ AB
Since, MK = BM
Therefore, ∠ MKB= ∠ MBK
But, ∠MBK=∠ABK ( Because it is given that BK is the angle bisector)
Therefore By the converse of Interior Alternatiove angle theorem,
KM ∥ AB ( Because ∠MBK and ∠ABK are the angle on lines AB and KM respectively by the same transversal BK)
