Question

E and F are representively the midpoints of equal sides AB and AC of triangle ABC show that BF =CE​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

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$\sf\underbrace{Question: }$

• E and F are representively the midpoints of equal sides AB and AC of triangle ABC show that BF = CE

$\sf\underline\red{Given:}$

• AB = AC .....(1)
• E is the mid-point of AB & F is the mid-point of Ac.

$\sf\underline\purple{To\:Prove:}$

• BF = CE

$\sf\underline\orange{Solution:}$

Given

• $\sf{⟹}$$\sf{AB\:=\:AC}$

• $\sf{⟹}$$\sf\dfrac{1}{2}$$\sf{AB\:=}$$\sf\dfrac{1}{2}$

• $\sf{⟹}$$\sf{AE\:=\:AF}$

In ∆ABF and ∆ACE,

• $\sf{⟹}$$\sf{AB\:=\:AC}$

• $\sf{⟹}$$\sf{∠A\:=\:∠A}$

• $\sf{⟹}$$\sf{AF\:=\:AE}$

So, ∆ABF ≈ ∆ACE,

• $\bf\pink{∴\:BF\:=\:CE\:.....(CPCT)}$

$\bf\underline{Hence\:Proved}$

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