ABC and DBC are two isosceles triangles on the same base BC.show that angleABD is equal angle ACD.
Hi!
Here is the answer to your question.
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Given: ∆ABC and ∆DBC are two isosceles triangles on the same base BC.
To prove: ∠ABD = ∠ACD
Proof: In ∆ ABC,
AC = AB (∆ABC is an isosceles triangle)
⇒∠ABC = ∠ACB … (1) (Equal sides have equal angles opposite to them)
In ∆ DBC,
DC = DB (∆DBC is an isosceles triangle)
⇒ ∠DBC = ∠DCB … (2) (Equal sides have equal angles opposite to them)
Adding (1) and (2), we get
∠ABC = ∠DBC = ∠ACB + ∠DCB
⇒ ∠ABD = ∠ACD
Cheers!