In a triangle MNK MN = NK. Points A, B and C are the midpoints of sotron MK, MN and NK, respectively.

In a triangle MNK MN = NK. Points A, B and C are the midpoints of sotron MK, MN and NK, respectively. Prove that the angle MAB is equal to the angle KAC.

If in a triangle MNK MN = NK, A, B and C are the midpoints of the sides MK, MN and NK, then:

MB = BN = NC = CK;

MA = AK;

<M = <K.

Hence it follows that triangle MNA is equal to triangle ANK.

If triangle MNA is equal to triangle ANK, points A, B and C are midpoints of sides MK, MN and NK, respectively, then AB = AC.

Received:

AB = AC;

MB = CK;

MA = AK.

Hence it follows that triangle MBA is equal to triangle ACK.

If triangle MBA is equal to triangle ACK, then angle MAB is equal to angle KAC.