Question

ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and
AB respectively. Show that these altitudes are equal.

Answer 1

Answer:

these drawn altitudes are equal beacause both are of 90 degerr

Answer 2

Answer:

We need to first take a suitable combination of triangles,and prove that they are congruent.After proving that they are congruent , we can make use of cpct.

Let's take the triangles BFC and BEC.

BF=EC (as AB=AC because ABC is an isoceles triangle) S

Angle BFC = Angle BEC = 90 (altitudes,given) A

BC=BC (common side) S

Therefore,Triangle BFC is congruent to Triangle BEC by SAS criterion.

Now,

CF=BE (Corresponding parts of congruent triangles are equal/cpct)

Hence proved.

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