Question
A diagonal of a parallelogram divides it into two congruent triangles.
Answer: Option A
:
A
Suppose ABCD is a parallelogram and BD is the diagonal.
There are two triangles - Δ ABD and Δ CDB
In Δ ABD and Δ CDB,
AD = BC (opposite sides of a parallelogram are equal)
AB = CD (opposite sides of a parallelogram are equal)
BD is common
∴ By SSS criterion of congruency,
Δ ABD ≅ Δ CDB
Hence, the given statement is true.
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:
A
Suppose ABCD is a parallelogram and BD is the diagonal.
There are two triangles - Δ ABD and Δ CDB
In Δ ABD and Δ CDB,
AD = BC (opposite sides of a parallelogram are equal)
AB = CD (opposite sides of a parallelogram are equal)
BD is common
∴ By SSS criterion of congruency,
Δ ABD ≅ Δ CDB
Hence, the given statement is true.
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