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# In Fig. 5.2, we have : AC = XD, C is the mid-point of AB and D is the mid-point of XY. Using an Euclid’s axiom, show that AB = XY

**Solution:**

Given, AC = XD

C is the midpoint of AB

D is the midpoint of XY

We have to show that AB = XY using Euclid's axiom.

According to Euclid’s axiom,

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

Since C is the midpoint of AB

AB = 2AC

AC = AB/2

Since D is the midpoint of XY

XY = 2XD

XD = XY/2

We know, AC = XD

So, AB/2 = XY/2

Therefore, AB = XY

**✦ Try This: **In the figure, ∠1 = 60° and ∠6 = 120°. Show that the lines m and n are parallel.

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

**NCERT Exemplar Class 9 Maths Exercise 5.3 Sample Problem 4**

## In Fig. 5.2, we have : AC = XD, C is the mid-point of AB and D is the mid-point of XY. Using an Euclid’s axiom, show that AB = XY

**Summary:**

In Fig. 5.2, we have : AC = XD, C is the mid-point of AB and D is the mid-point of XY. Using Euclid’s sixth axiom, it is shown that AB = XY

**☛ Related Questions:**

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- It is known that x + y = 10 and that x = z. Show that z + y = 10. Solve using Euclid’s axiom
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