Observe the figure clearly.
To Prove: KA = KC
Proof:
Consider the triangles [tex]\Delta KAB , \Delta KCB[/tex]
KB = KB (Common side)
[tex]\angle KAB = \angle KCB[/tex] (each angle is of 90 degree)
[tex]\angle ABK = \angle KBC[/tex] (As BY bisects angle ABC)
Therefore, [tex]\Delta KAB \cong \Delta KCB[/tex]
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.
ASA Congruence Theorem can Yash use to prove the triangles congruent.
Given
Yash wants to prove that KA=KC.
To do that, he decides to prove that △KAB≅△KCB.
It states that if two angles and the included side of one triangle are congruent to two angles and included side of another triangle, then the two triangles are congruent.
Here, triangle △KAB≅△KCB
KB = KB (Common side)
In the triangle △KAB≅△KCB each angle is 90 degrees.
∠ABK = ∠KBC
Therefore,
△KAB≅△KCB
Hence proved
Hence, ASA Congruence Theorem can Yash use to prove the triangles congruent.
To know more about ASA postulates click the link given below.
https://brainly.com/question/3451297
