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Standard IX
Maths
Criteria for Congruence of Triangles
Question
In figure, $$ADBC$$ is a quadrilateral in which $$\angle ABC = \angle ABD$$ and $$BC = BD$$ then show that $$\Delta ABC \cong \Delta ABD$$.
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Solution
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In $$\Delta ABC$$ and $$\Delta ABD$$
$$\angle ABC = \angle ABD$$ (given)
$$BC = BD$$ (given)
$$AB = AB$$ (common side)
similarly, $$\Delta ABC \cong \Delta ABD$$
(By SAS congruency property)
Hence proved.
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