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CBSE Class 9 Mathematics Question 13 of 21

Triangles — Question 5

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Question 5

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

ABC and DBC are two isosceles triangles on the same base BC. Show that ∠ABD = ∠ACD. NCERT Class 9 Mathematics CBSE Solutions.
Answer

Given :

ABC and DBC are isosceles triangles.

Join AD.

ABC and DBC are two isosceles triangles on the same base BC. Show that ∠ABD = ∠ACD. NCERT Class 9 Mathematics CBSE Solutions.

In △ DAB and △ DAC,

⇒ AB = AC (Given)

⇒ BD = CD (Given)

⇒ AD = AD (Common side)

∴ △ ABD ≅ △ ACD (By S.S.S. congruence rule)

We know that,

Corresponding sides of congruent triangles are equal.

∴ ∠ABD = ∠ACD (By C.P.C.T.)

Hence, proved that ∠ABD = ∠ACD.