Eric Nicholas K's answer to Sai's Junior College 1 H2 Maths Singapore question.
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We only need two conditions to prove that ABCD is a parallelogram.
One, the direction of the vector AB (line AB) is the same as that of the vector DC (line DC). When two direction vectors are the same, the two lines are parallel.
Two, the distance AB must also be the same as the distance DC.
Once this is achieved, you will realise that no matter what, the other two lines AD and BC will also be parallel and equal in length. Hence, we only need the two conditions above to prove that ABCD is a parallelogram.
If the diagonals are equal in length, then the shape is definitely a rectangle. We cannot prove, however, that ABCD is a square; we will need another condition that AB = AD.
One, the direction of the vector AB (line AB) is the same as that of the vector DC (line DC). When two direction vectors are the same, the two lines are parallel.
Two, the distance AB must also be the same as the distance DC.
Once this is achieved, you will realise that no matter what, the other two lines AD and BC will also be parallel and equal in length. Hence, we only need the two conditions above to prove that ABCD is a parallelogram.
If the diagonals are equal in length, then the shape is definitely a rectangle. We cannot prove, however, that ABCD is a square; we will need another condition that AB = AD.
Date Posted:
5 years ago
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