Show that a diagonal divides a parallelogram into two triangles of equal area.
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I have attached a file which has the figure.
given- ABCD is a ||gm(parallelogram)
To prove - ΔADB ≅ ΔCBD
Proof-
as ABCD is a || gm, AD || BC
∴∠ABD = ∠CBD(alternate.interior.∠s)
also AB || DC
∴∠ABD = ∠ CDB(alternate.interior.∠s)
DB = BD(common)
∴ΔADB ≅ ΔCBD
∴ar(ADB) =ar(CBD)
given- ABCD is a ||gm(parallelogram)
To prove - ΔADB ≅ ΔCBD
Proof-
as ABCD is a || gm, AD || BC
∴∠ABD = ∠CBD(alternate.interior.∠s)
also AB || DC
∴∠ABD = ∠ CDB(alternate.interior.∠s)
DB = BD(common)
∴ΔADB ≅ ΔCBD
∴ar(ADB) =ar(CBD)
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Answered by
31
Hope this helps you!!
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