In triangle ABC, sides AB and BC are equal, and BH is a bisector. Prove that Triangle ABH = Triangle CBH.

| September 1, 2021 | education

Consider triangles ABH and CBH.
Before proving that triangles ABH and CBH are equal, let us pay attention to the first criterion for the equality of triangles.
According to the first sign of equality of triangles, if two sides and the angle between them of one triangles are respectively equal to two sides and the angle between them of another triangle, then these triangles are equal.
1.) By the condition of the problem, the sides AB and BC, respectively, in triangles ABH and CBH are equal.
2.) The BH side is the common side for these triangles ABH and CBH.
3.) By the condition of the problem, the side BH is a bisector.
Thus, the value of the angle ABH is equal to the value of the angle CBH.
That is, in the considered triangles ABH and CBH, the angles between two identical sides are equal.
4.) Thus, according to the first criterion for the equality of triangles, it is proved that triangles ABH and CBH are equal.



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