Respuesta :

Answer:

The proof is given below.

Step-by-step explanation:

  • IMPORTANT: angle bisector theorem

this theorem says that, if a point is on the angular bisector of an angle, then it is equidistant from the sides of the angle.

  • here, since X lies on the angular bisector of angle MBC and BCN , it will be equidistant from the sides BM and CN ( by using above theorem) .
  • since the line BM also passes through A and the line CN also passes through A, we can say that X is equidistant from the sides AM and AN also.
  • converse of angle bisector theorem : if a point is equidistant from the sides of an angle, then it lies on the angular bisector of that angle.
  • by using this converse of angle bisector theorem, we can say that X lies on the angular bisector of angle A.
  • hence, it is proved that X is on the bisector of ANGLE A.

(the proof of  angle bisector theorem can be explained, but it is difficult to type the whole thing. so watch this video for the proof of this theorem :  https://youtu.be/6GS4lS4btNI    )

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