Question

Prove that diagonals of a trapezium intersect each other in the same ratio

Answer 1

Given:  A trapezium.

To find:  Prove that diagonals of a trapezium intersect each other in the same ratio.

Solution: ​  

•  Lets consider a trapezium ABCD, where the two sides AB and CD are parallel to each other.

• Also, consider the intersection point of the diagonals be X.

• Construction:

• Lets draw XZ parallel to AB through O which meets AD at Z.

• Now in triangle ADC, we have ZX parallel to DC.

• So, therefore

             AZ/ZD = AX/XC

• Now in triangle DAB,  ZX parallel to AB.

• So, therefore

             AZ/ZD = BX/XD

• So from above two ratios,

             AX/XC= BX/XD

​  

Answer:

               AX/XC= BX/XD ........... hence proved.

Answer 2

Answer:

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