The bisector BD is drawn in an isosceles triangle ABC with base AC.
| January 28, 2021 | education
The bisector BD is drawn in an isosceles triangle ABC with base AC. Prove that point M taken on this bisector is equidistant from vertices A and C.
Based on the properties of an isosceles triangle:
The bisector in an isosceles triangle is the median and height.
So it divides the base in half.
AD = DC.
Considering that it is the same and the height means the CDA and ВDС triangles are equal and are rectangular with a common side ВD.
It follows that any point located on the bisector will be equally distant from the vertices A and C.
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