Question
In the adjoining figure, $\triangle\text{ABC}$ is an isosceles triangle in which AB = AC. If E and F be the midpoints of AC and AB respectively, prove that BE = CF.
✓
Answer
Given: $\triangle\text{ABC}$ is an isosceles triangle in which AB = AC.
E and F are the midpoints of AC and AB respectively.
To prove: BE = CF
Proof: IN $\triangle\text{BCF}$ and $\triangle\text{CBE},$
BC = BC (common)
BF = CE (Half of equal sides AB and AC)
$\angle\text{CBF}=\angle\text{BCF}$ (Angles opposite to equal sides)
$\triangle\text{BCF}\cong\triangle\text{CBE}$ (SAS condition)
CF = BE (c.p.c.t.)
or BE = CF
Hence proved.
E and F are the midpoints of AC and AB respectively.
To prove: BE = CF
Proof: IN $\triangle\text{BCF}$ and $\triangle\text{CBE},$
BC = BC (common)
BF = CE (Half of equal sides AB and AC)
$\angle\text{CBF}=\angle\text{BCF}$ (Angles opposite to equal sides)
$\triangle\text{BCF}\cong\triangle\text{CBE}$ (SAS condition)
CF = BE (c.p.c.t.)
or BE = CF
Hence proved.
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