In the Fig. 5.11, if OX = 1/2 XY, PX = 1/2 XZ and OX = PX, show that XY = XZ..Solve using Euclid’s axiom

Solution:

The figure represents a triangle XYZ.

The points O and P lie on the sides XY and XZ.

Given, OX = XY/2 --------------- (1)

PX = XZ/2 ------------------------- (2)

Also, OX = PX —------------------- (3)

We have to show that XY = XZ.

From (1), XY = 2OX

This implies O is the midpoint of XY

So, XY = 2OX = 2OY ---------------------- (4)

From (2), XZ = 2PX

This implies P is the midpoint of XZ

So, XZ = 2PX = 2PZ ---------------------- (5)

According to Euclid’s axiom,

Things which are double of the same thing are equal to one another

Using (3) in (4) and (5), we get

2OX = 2PX

Therefore, XY = XZ

✦ Try This: If DE||QR and AP and BP are bisectors of ∠EAB and ∠RBA respectively. Find ∠APB.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 5

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NCERT Exemplar Class 9 Maths Exercise 5.3 Problem 11

In the Fig. 5.11, if OX = 1/2 XY, PX = 1/2 XZ and OX = PX, show that XY = XZ..Solve using Euclid’s axiom

Summary:

In the Fig. 5.11, we have OX = 1/2 XY, PX = 1/2 XZ and OX = PX. We observe that O and P are the midpoint of XY and XZ. By using Euclid’s axiom, it is shown that XY = XZ

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