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Question
Solve the following question using appropriate Euclid’s axiom:
In the following figure, if OX = `1/2` XY, PX = `1/2` XZ and OX = PX, show that XY = XZ.
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Solution
Given OX = `1/2` XY
⇒ 2OX = XY ...(i)
PX = `1/2` XZ
⇒ 2PX = XZ ...(ii)
And OX = PX ...(iii)
According to Euclid’s axiom, things which are double of the same things are equal to one another.
On multiplying equation (iii) by 2, we get
2OX = 2PX
XY = XZ ...[From equations (i) and (ii)]
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