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Congruence — Maths STD 7 — Question

Maharashtra BoardEnglish MediumSTD 7MathsCongruence3 Marks
Question
In the given figure, $\triangle\text{ABC}$ is an isosceles triangle in which AB = AC. If AB and AC are produced to D and E respectively such that BD = CE, prove that BE = CD.
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Answer

Given: $\triangle\text{ABC}$ is an isosceles triangle in which AB = AC.
AB and AC are produced to D and E respectively such that BD = CE.
BE and CD are joined.
To prove: BE = CD.
Proof: Ab = Ac and BD = CE
Adding we get:
AB + BD = AC + CE
AD = AE
Now, in $\triangle\text{ACD}$ and $\triangle\text{ABE}$
AC = AB (given)
$\angle\text{A}=\angle\text{A}$ (common)
$\triangle\text{ACD}\cong\triangle\text{ABE}$ (SSA condition)
CD = BE (c.p.c.t)
Hence, BE = CD.

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