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ABC is an isosceks triangk in which altitudes BE and CF P,re drawn to • equal sides AC and AB respectively (see figure ). Show that these altitudes are equal.

ABC is an isosceks triangk in which altitudes BE and CF P,re drawn to • equal sides AC and AB respectively (see figure ). Show that these altitudes are equal.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60782 Points
2 years ago
In A ABC, AB = AC => LACB = LABC [Given] ...(i) [Angles opposite to equal sides of a triangle are equal.] Consider triangles BFC and BCE, We have LFBC = LECB [From (i)] BC = CB [Common] LBFC = LCEB .MJCF ::ACBE CF = BE. [90° each] [AAS rule) Hence, altitudes to the equal sides of a triangle are equal.

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