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In the given figure,BE and CF …

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In the given figure,BE and CF are two equal altitudes of triangle ABC.Show that triangle ABE is congruent to triangle ACF and AB =AC

    • Posted by Badboi Vicky 6 years, 4 months ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Sia ? 6 years, 4 months ago

    Given : ABC is a triangle in which altitude BE and CF to side AC and AB are equal.
    To Prove : {tex}\triangle \mathrm { ABE } \cong \triangle \mathrm { ACF }{/tex}

    1. AB = AC i.e. {tex}\triangle{/tex}ABC is an isosceles triangle.
      Proof : BE = CF ...... [Given]
      ∠BAE = ∠CAF ...... [Common]
      ∠AFB = ∠AFC ....... [Each 90o]
      {tex}\therefore{/tex} {tex}\triangle \mathrm { ABE } \cong \triangle \mathrm { ACF }{/tex} ........ [By AAS property]
    2. {tex}\triangle A B E \cong \triangle A C F{/tex} ....... [As proved]
      {tex}\therefore{/tex} AB = AC . . .[c.p.c.t.]
      ​​​​​​​{tex}\therefore{/tex} {tex}\triangle{/tex}ABC is an isosceles triangle.

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