In ABC, with AB=AC, prove that the altitude from the vertex A bisects the side BC.


Answer:


Step by Step Explanation:
  1. We know that ABC is an isosceles triangle in which AB=AC.

    Let AD be the altitude from the vertex A on the side BC.

    As the altitude from a vertex to the opposite side is perpendicular to the opposite side. ADBC Let us now represent the above situation with the help of a figure.
      A B C D
  2. We need to prove that BD=DC.
  3. In the right-angled ADB and ADC, we haveAD=AD[Common]AB=AC[Given]
  4. As corresponding parts of congruent triangles are equal, we haveBD = DC
  5. Thus, in an isosceles triangle, the altitude from the vertex bisects the base.

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