Question

Prove that the diagonal of a parallelogram divides
it into two triangles of equal area.​

Answer 1

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Answer 2

Step-by-step explanation:

Here, ABCD is a parallelogram and BD is diagonal.

In △ADB and △CBD

AD∥BC

⇒  ∠ADB=∠CBD               [ Alternate angles ]

Also AB∥DC

⇒  ∠ABD=∠CDB               [ Alternate angles ]

⇒  DB=BD                           [ Common side ]

∴  △ADB≅△CBD              [ By SAS congruence rule ]

Since congruent figures have same area.

∴  ar(ADB)=ar(CBD)                      [ Hence, proved ]

∴  We have proved that a diagonal divides a parallelogram  into two triangles of equal area.

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