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Standard IX
Maths
Congruence of Triangles
Question

In a triangle $$ ABC , AB = AC $$. Points G on AB and D on AC are such that $$AE = AD $$ prove that triangles BCD and CBE are congruent

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Solution
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In the figure $$AB = AC $$ (data )
$$\therefore \angle ABC = \angle ACB $$
[ Base angles of an isosceles triangles ]
$$AB = AC $$ (data )
$$AE = AD $$ (data )
$$AB - AE = AC - AD $$ (Axiom 3)
$$ BE = DC $$
In $$\bigtriangleup BCD $$ and $$\bigtriangleup CBE $$
$$ \angle BCD = \angle EBC $$
$$BE = DC $$ (proved )
$$ BC = BC $$ (Common side )
$$ \therefore \bigtriangleup BCD = \bigtriangleup CBE $$ [ S AS postulate ]

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