Question

7. ABC is an isosceles triangle with AB - AC and D, E, F are the
mil points of the sides BC, CA, AB respectively. Show that AD
and FE bisect each other at right angles.

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Answer 1

Answer:

Since D,E and F are the mid-points of sides BC,CA and AB respectively.

∴AFDE is a parallelogram

⇒AF=DE and AE=DF

⇒

2

1

AB=DE and

2

1

AC=DF

⇒DE=DF [∵AB=AC]

⇒AE=AF=DE=DF

⇒AEDF is a rhombus

⇒ AD and FE bisect each other at the right angle.