Question

prove that the bisectors of the base angle of an isosceles triangle are equal

Answer 1

Look at the figure attached

Here ABC is an isocelous triangle with angle A= angle B
CM and BN are the angle bisectors
So now we observe tri(BMC) and tri(BNC)

1) BC = BC
2) ang(MBC) = ang(NCB)
3) ang(NBC) = ang(MCB)

so by ASA congruency condition the triangles are congruent
and hence
BN = CM
proved

Answer 2

Question:-

The correct question is:-Prove that the bisectors of the base angles of an isosceles triangle are equal.

Step-by-step explanation:

solution:-

In △ABC,

AB=AC [Given]

∴∠C=∠B .....(i) [angles opp. to equal sides are equal]

⇒ 1/2<C = 1/2<B.

∠BCF=∠CBE.......(ii)

Now,In △BCE and △CBF,

=>∠C=∠B [From (i)]

=>∠BCF=∠CBE [From (ii)]

=>BC=BC [Common]

△BCE≅△CBF [AAS]

⇒BE=CF [cpct].

see the above picture...

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