Question

prove that a diagonal of a parallelogram divides it into the two congruent triangles
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Answer 1

Step-by-step explanation:

[Consider the attached figure]

Given: ABCD is a Parallelogram. in which AC is a diagonal.

Required to Proof: Diagonal of a parallelogram divides it into two congruent triangles.

Proof: Diagonal AC of the parallelogram ABCD divides it into two triangles ΔABC and ΔACD.

Now,

In  ΔABC and ΔACD

i) AB = DC  [∵Opposite side of a parallelogram are equal and parallel]

ii) BC = AD  [∵Opposite side of a parallelogram are equal and parallel]

iii) AC = AC  [∵Common side]

∴ ΔABC ≅ ΔACD  [by S-S-S rule of congruence]

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Answer 2

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