Given is an isosceles triangle ABC (AB = BC). on the BC side we took points K and M (point K lies on BM).

| April 11, 2021 | education

Given is an isosceles triangle ABC (AB = BC). on the BC side we took points K and M (point K lies on BM). these points are connected by segments with apex A. it turned out that KM = AM and the angle BAC is equal to the angle MAC. prove that the angles when equipping the triangle ABC are more than 60 degrees.

Let us prove that the angle ABC is acute and less than 60º, then the angles at the base will be more than 60º.

Suppose that angle B in triangle ABC is obtuse or equal to 60º.

Then, the AC side is greater (or equal to) the AB = BC side, which means that the AM side is greater than the BM side and cannot be equal to KM.

Hence it follows that the angle ABC cannot be obtuse and more than 60º, since according to the condition KM = AM.

The AC side is smaller than the AB and BC sides.

Therefore, angles A and C in triangle ABC are greater than 60º.



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