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Asked: 2023-03-27T05:50:24+00:00 In:

ABC and DBC are two isosceles triangles on the same base BC (see Figure). Show that ∠ ABD = ∠ ACD.

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ABC and DBC are two isosceles triangles on the same base BC (see Figure). Show that ∠ ABD = ∠ ACD.

How to check the angle sum property of triangle.
TRIANGLES Solutions for Class 9th Maths.
9th Maths EXERCISE 7.2,Page No:124, Questions No:5.
Class 9th ,NCERT Books for Session 2023-2024, based on CBSE Board.

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      ABC and DBC are two isosceles triangles on the same base BC (see Figure). Show that ∠ ABD = ∠ ACD.

      In ΔABC,
      AB = AC [∵ Given]
      ∠ABC = ∠ACB …(1) [∵ Angles opposite to equal sides are equal]
      In ΔDBC,
      DB = DC [∵ Given]
      ∠DBC = ∠DCB …(2) [∵ Angles opposite to equal sides are equal]
      Adding equation (1) and (2), we get
      ∠ABC + ∠DBC = ∠ACB + ∠DCB
      ⇒ ∠ABD = ∠ACD.

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