Question

if the bisectors of the vertically angle of a ∆ bisects the base of the ∆ then then the ∆ is a isosceles​

Answer 1

Step-by-step explanation:

We are given a point D on side BC of a ∆ ABC such that

∠ BAD = ∠ CAD and BD = CD

We want to prove that AB =AC.

Now we produce our line AD to E , As AD = DE , Then join CE.

according to our figure :

Now In ∆ ABD and ∆ ECD

BD = CD ( Given )

AD = ED ( By construction )

∠ ADB = ∠ EDC ( Vertically opposite angles )

Hence

∆ ABD ≅ ∆ ECD ( By SAS rule )

So,

AB = EC -------------------- ( 1 ) ( BY CPCT )

And

∠ BAD = ∠ CED -------------------- ( 2 ) ( BY CPCT )

So we get

∠ CED = ∠ CAD ( As given ∠ BAD = ∠ CAD )

So from base angle theorem we get

AC = EC

So,

AB = AC ( As we know from equation 1 , AB = EC )

Hence

In ∆ ABC , AB = AC , So ∆ ABC is a isosceles triangle . ( Hence proved )

Answer 2

What you need is in the page below.

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