Question

ABC is an isosceles triangle in which altitudes
BE and CF are drawn to equal sides AC and AB
respectively (see Fig. 7.31). Show that these
altitudes are equal.
1.D
and​

Answer 1

Given: A triangle ABC in which AB=AC and BE and CF are drawn to equal side AC and AB respectively.

To prove: BE=CF

Proof: We know that angle opposite to equal side are equal.

AB=AC

So, angle CBF = angle BCE ----- eq. 1

Now, in triangles BCF and CBE ,

BC=BC [common]

angle CBF = angle BCE [proved in eq.1]

angle BFC = angle CEB [both equal to90°]

So, triangle BCF congurent to triangle CBE.

Hence , BE=CF [CPCT]

therefore , BE=CF