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Question
In the given figure, by how much should the length of DC be increased so that △ ABC ≅ △ DBC?
Given that AB= 6 cm, AC= 5cm, BC= 4cm and BD= 6cm.
In the given figure, by how much should the length of DC be increased so that △ ABC ≅ △ DBC?
Given that AB= 6 cm, AC= 5cm, BC= 4cm and BD= 6cm.
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Solution
The correct option is C 2 cm
If triangles ABC and DBC are congruent, then their corresponding sides should be equal to each other.
This means
AB= DB .................(1)
BC= BC .................(2)
AC= DC .................(3)
The first 2 conditions are already satisfied as AB= DB= 6cm and BC = BC= 4 cm
AC= 5 cm
DC= 3 cm
Thus, to become equal, DC should increase by (AC- DC) = 5 - 3 = 2 cm
2 cm
If triangles ABC and DBC are congruent, then their corresponding sides should be equal to each other.
This means
AB= DB .................(1)
BC= BC .................(2)
AC= DC .................(3)
The first 2 conditions are already satisfied as AB= DB= 6cm and BC = BC= 4 cm
AC= 5 cm
DC= 3 cm
Thus, to become equal, DC should increase by (AC- DC) = 5 - 3 = 2 cm
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