Question

3.
A
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.

​

Answer 1

Answer:

Here is the correct answer

Step-by-step explanation:

Ans. ΔABC is an isosceles triangle.

∴ AB = AC

⇒ ∠ACB = ∠ABC

[∴ Angles opposite to equal sides are equal]

Now, in ΔBEC and ΔCFB, we have

∠EBC = ∠FCB

[Proved]

BC = CB

[Common]

and ∠BEC = ∠CFB

[Each = 90°]

∴ ΔBEC ≌ ΔCFB

[Using ASA criteria]

⇒ Their corresponding parts are equal.

i.e. BE = CF