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  • Solve each of the following question using appropriate Euclid’s axiom: In the Fig. 5.11, if OX equal to 1 divided 2 XY, PX equal to 1 divided 2 XZ and OX equal to PX, show that XY equal to XZ.

Solve each of the following questions using appropriate Euclid’s axiom: In Fig. 5.11, if OX=0.5XY, PX=0.5XZ and OX = PX, show that XY = XZ.

Answers (1)

Given that:

OX = 0.5 XY, PX = 0.5 XZ, OX = PX

To prove: XY = XZ

OX = 0.5XY                 ;           PX = 0.5 XZ

2OX = XY … (1)        ;           2PX = XZ … (2)

OX = PX  … (3)                     (Given)

Euclid's axiom says that things which are double of the same things are equal to one another.

Hence from equation (1), (2), (3)

2OX = 2PX

XY = XZ

Hence proved.

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