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CBSE Class 9 Mathematics Question 11 of 21

Triangles — Question 3

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Question 3

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.

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. NCERT Class 9 Mathematics CBSE Solutions.
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.