1.

ΔABC and ΔDBC are two isosceles triangles on the same base BC (see figure). Show that ∠ABD =∠ACD.

Answer»

Use the result that angles opposite to equal sides of a triangle are equal in both ∆ABC & ∆DBC and then add these results to SHOW the required result.


SOLUTION:

Given: ABC and DBC are two ISOSCELES triangles.

To Prove: ∠ABD = ∠ACD

Proof: In ΔABC, AB =AC. (given)

∠ACB= ∠ABC......(1)

[Since angles opposite to equal sides of a triangle are equal]


In ∆ DBC,

DB=DC (given)

∠DCB = ∠DBC......(2)

[Since angles opposite to equal sides of a triangle are equal] On


adding eq 1 & 2 , We get

∠ACB+ ∠DCB= ∠ABC+ ∠DBC

∠ACD= ∠ABD


Hence, ∠ACD = ∠ABD


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