If the altitudes from the two vertices of a triangle to the opposite sides are equal, prove that the triangle is isosceles.


Answer:


Step by Step Explanation:
  1. Let BD and CE be the altitudes from the vertices B and D of ABC.

    As the altitude of a triangle is perpendicular to the opposite side, we have BDAC and CEAB Also, we are told that the altitudes are of equal length. BD=CE
      A B C E D
  2. We need to prove that AB=AC.
  3. In ADB and AEC, we have BD=CE[Given]BAD=CAE[Common]ADB=AEC=90[BDAC and CEAB] ADBAEC[By AAS criterion]
  4. As the corresponding parts of congruent triangles are equal, we have AB=AC.
    Hence, ABC is isosceles.

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