ABC and DBC are two isosceles triangles on the same base BC. Show that

1.	ABC and DBC are two isosceles triangles on the same base BC. Show that ∠ABD = ∠ACD.
Answer» Data: ABC and DBC are two isosceles triangles on the same base BC. To Prove: ∠ABD = ∠ACD Proof: In ∆ABC, AB = AC, ∴ Opposite angle ∠ABC = ∠ACB …………. (i) Similarly in ∆BDC, BD = DC. Opposite angle ∠DBC = ∠DCB ………….. (ii) From (i) and (ii), ∠ABC = ∠ACB Adding ∠DBC and ∠DCB on both sides, ∠ABC + ∠DBC = ∠ABD ∠ACB + ∠DCB = ∠ACD Equals are added to equal angles. ∴ ∠ABD = ∠ACD.

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

Answer»

Data: ABC and DBC are two isosceles triangles on the same base BC.

To Prove:

∠ABD = ∠ACD

Proof:

In ∆ABC, AB = AC,

∴ Opposite angle

∠ABC = ∠ACB …………. (i)

Similarly in ∆BDC, BD = DC.

Opposite angle

∠DBC = ∠DCB ………….. (ii)

From (i) and (ii),

∠ABC = ∠ACB

Adding ∠DBC and ∠DCB on both sides,

∠ABC + ∠DBC = ∠ABD

∠ACB + ∠DCB = ∠ACD

Equals are added to equal angles.

∴ ∠ABD = ∠ACD.