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Observe the figure clearly.
To Prove: KA = KC
Proof:
Consider the triangles
KB = KB (Common side)
(each angle is of 90 degree)
(As BY bisects angle ABC)
Therefore,
By AAS congruence Theorem which states:
"If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent".
Hence, the given triangles are congruent by AAS congruence criteria.