Mathematics
ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively see Fig. Show that these altitudes are equal.
Triangles
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Answer
Given :
Δ ABC is an isosceles triangle with AB and AC as equal sides.
In Δ AEB and Δ AFC,
⇒ ∠AEB = ∠AFC (Each equal to 90° as BE and CF are altitudes)
⇒ ∠A = ∠A (Common angle)
⇒ AB = AC
∴ Δ AEB ≅ Δ AFC (By A.A.S. congruence rule)
We know that,
Corresponding parts of congruent triangles are equal.
∴ BE = CF (By C.P.C.T.)
Hence, proved that BE = CF.
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