Prove that the perpendiculars drawn from the vertices of equal angles of an isosceles triangle to the opposite sides are equal.


Answer:


Step by Step Explanation:
  1. Let ABC be an isosceles triangle with B = C. Now, let us draw the perpendiculars from B and C to the opposite sides.

    Thus, BDAC and CEAB.
      A B C E D
  2. We need to prove that BD=CE.
  3. In BCD and BCE, we have BC=BC[Common]BDC=CEB[Each 90]BCD=CBE[As ABC is an isosceles triangle.]
  4. As the corresponding parts of congruent triangles are equal, we have BD = CE
  5. Thus, the perpendiculars drawn from the vertices of equal angles of an isosceles triangle to the opposite sides are equal.

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