ABCD is a parallelogram with diagonal AC. If a line XZ is drawn such that XZ∥AB and cuts AC at Y, prove that BX/XC=AZ/ZD.

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Solution

Given: AB || XZ

In ΔABC, AB || XY

Therefore BX/XC = AY/YC ….. (1)

In parallelogram ABCD, AB || CD

AB || CD || XZ

In ΔACD, CD || YZ

Therefore AY/YC = AZ/ZD ….( 2)

From (1) and (2)

BX/XC = AY/YC = AZ/ZD

So, BX/XC = AZ/ZD

Hence proved

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ABCD is a parallelogram with diagonal AC. If a line XZ is drawn such that XZ∥AB and cuts AC at Y, prove that BX/XC=AZ/ZD.

Given: AB || XZ In ΔABC, AB || XY Therefore BX/XC = AY/YC ….. (1) In parallelogram ABCD, AB || CD AB || CD || XZ In ΔACD, CD || YZ Therefore AY/YC = AZ/ZD ….( 2) From (1) and (2) BX/XC = AY/YC = AZ/ZD So, BX/XC = AZ/ZD Hence proved

Given: AB || XZ

In ΔABC, AB || XY

Therefore BX/XC = AY/YC ….. (1)

In parallelogram ABCD, AB || CD

AB || CD || XZ

In ΔACD, CD || YZ

Therefore AY/YC = AZ/ZD ….( 2)

From (1) and (2)

BX/XC = AY/YC = AZ/ZD

So, BX/XC = AZ/ZD

Hence proved