Question

draw a parallelogram ABCD on a card sheet. draw diagonal AC.write the names of vertices inside the triangle as shown in the figure.then cut is out.
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Answer 1

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Let ABCD be a parallelogram and consider its diagonal AC. Draw perpendiculars BK and DL on to AC. Prove that BK=DL.

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Solution

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THEOREMS AND PROBLEMS ON PARALLELOGRAMS – EXERCISE 4.3.3- Class IX

Given: ABCD is a parallelogram. BK and DL are perpendiculars drawn to diagonals AC.

It is given that in quadrilateral ABCD, DL and BK are perpendicular to AC.

ΔADC is congruent to ΔABC (Diagonal divides a parallelogram into two congruent triangles)

Therefore, Area ΔABC= Area ΔADC

That is

2

1

AC×BK=

2

1

AC×DL implies BK=DL.

Hence, BK=DL.

Answer 2

Q :Let ABCD be a parallelogram and consider its diagonal AC. Draw perpendiculars BK and DL on to AC. Prove that BK=DL.

Solution:

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THEOREMS AND PROBLEMS ON PARALLELOGRAMS – EXERCISE 4.3.3- Class IX

Given: ABCD is a parallelogram. BK and DL are perpendiculars drawn to diagonals AC.

It is given that in quadrilateral ABCD, DL and BK are perpendicular to AC.

ΔADC is congruent to ΔABC (Diagonal divides a parallelogram into two congruent triangles)

Therefore, Area ΔABC= Area ΔADC

That is  

2

1

​

AC×BK=

2

1

​

AC×DL implies BK=DL.

Hence, BK=DL.