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som dutt
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Asked: 2023-03-27T05:50:18+00:00 In:

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Figure). Show that (i) Δ ABE ≅ Δ ACF (ii) AB = AC, i.e., ABC is an isosceles triangle.

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ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Figure). Show that (i) Δ ABE ≅ Δ ACF (ii) AB = AC, i.e., ABC is an isosceles triangle.

What is the Side-Angle-Side (SAS) congruence criterion.
CBSE Board and Others state Board.
9th Maths EXERCISE 7.2, Page No:124, Questions No:4.
NCERT Books for Session 2023-2024 are based on CBSE Board.

class 9mathsncert
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    1. Best Answer
      ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Figure). Show that (i) Δ ABE ≅ Δ ACF (ii) AB = AC, i.e., ABC is an isosceles triangle.

      (i) In ΔABE and ΔACF,
      ∠AEB = ∠AFC [∵ Each 90]
      ∠A = ∠A [∵ Common]
      BE = CF [∵ Given]
      Hance, ΔABE ≅ ΔACF [∵ SAS Congruency Rule]

      (ii) In ΔABE ΔACF [∵ Proved above]
      AB = AC [∵ CPCT]
      Hence, ΔABC is an isosceles triangle.

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