Question

Yash wants to prove that KA=KC. To do that, he decides to prove that△KAB≅△KCB. Which theorem or postulate can Yash use to prove the triangles congruent?
Hypotenuse-Leg (HL) Congruence TheoremSide-Side-Side (SSS) Congruence PostulateAngle-Angle-Side (AAS) Congruence TheoremSide-Angle-Side (SAS) Congruence Postulate

Answer 1

Observe the figure clearly.

To Prove: KA = KC

Proof:

Consider the triangles $\Delta KAB , \Delta KCB$

KB = KB (Common side)

$\angle KAB = \angle KCB$ (each angle is of 90 degree)

$\angle ABK = \angle KBC$ (As BY bisects angle ABC)

Therefore, $\Delta KAB \cong \Delta KCB$

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.