ABC is an isosceles triangle in which altitudes BE and CF are drawn to

1.	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» Data: ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively To Prove: Altitude BE = Altitude CF. Proof: In ∆ABC, AB = AC and CF ⊥ AB, BE ⊥ AC. ∴ ∠BEC = ∠CFB = 90° (Data) Angles opposite to equal sides of an isosceles triangles are equal. BC is common. ∴ ∆BEC ≅ ∆CFB (ASA postulate) ∴ BE = CF.

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»

Data: ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively

To Prove: Altitude BE = Altitude CF.

Proof:

In ∆ABC,

AB = AC and CF ⊥ AB,

BE ⊥ AC.

∴ ∠BEC = ∠CFB = 90° (Data)

Angles opposite to equal sides of an isosceles triangles are equal.

BC is common.

∴ ∆BEC ≅ ∆CFB (ASA postulate)

∴ BE = CF.