Question

E and F are respectively the mid-points of equal sides AB and AC of triangle ABC.Refer to the figure and show that BF=CE..........​

Answer 1

≡QUESTION≡

E and F are respectively the mid-points of equal sides AB and AC of triangle ABC. Prove that BF = CE.

                                                   

║⊕ANSWER⊕║

In Δ ABF  and ΔACE

AB = AC ( Given)

∠ A = ∠A (Common angle)

AF = AE (Halves of equal sides are also equal) (1/2 AB = 1/2 AC)

∴ΔABF ≅ ΔACE  ( SAS congruency criteria)

BF = CE (CPCT)

                                                   

Answer 2

$\huge\underline\mathrm{Solution-}$

Given :

• AB = AC

• E and F are the midpoints of sides AB and AC respectively.

To prove :

• BF = CE

Proof :

It is given that AB = AC

$\therefore$ $\dfrac{1}{2}$ AB = $\dfrac{1}{2}$ AC

$\implies$ AE = AF [ °•° E and F are the midpoints of AB and AC respectively ]

In ∆ABF and ∆ACE

• AB = AC ( given )
• AE = AF ( proved above )
• $\angle{A}$ = $\angle{A}$ ( common )

$\therefore$ ∆ABF ≅ ∆ACE ( by SAS criteria )

$\implies$ $\huge{\boxed{\sf{BF\:=\:CE}}}$

Hence proved!