# In Fig.5.12, we have AB = BC, M is the mid-point of AB and N is the mid- point of BC. Show that AM = NC. Solve using Euclid’s axiom

**Solution:**

The figure represents two line segments AB and BC.

Given, AB = BC ------------------- (1)

M is the midpoint of AB

N is the midpoint of BC

We have to show that AM = NC

Since M is the midpoint of AB we get

AB = 2AM = 2BM

AM = BM = AB/2 ----------------------- (2)

Since N is the midpoint of BC, we get

BC = 2BN = 2NC

BC = BN = NC/2 ----------------------- (3)

By using Euclid’s axiom,

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

Multiplying (1) by 1/2 on both sides, we get

AB/2 = BC/2

From (2) and (3),

BM = BN

AM = NC

Therefore, it is proved that AM = NC

**✦ Try This:** Points A and B have coordinates (3,5) and (x,y) respectively. The mid-point of AB is (2,3). Find the values of x and y.

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

**NCERT Exemplar Class 9 Maths Exercise 5.3 Problem 12(i)**

## In Fig.5.12, we have AB = BC, M is the mid-point of AB and N is the mid- point of BC. Show that AM = NC. Solve using Euclid’s axiom

**Summary:**

In Fig.5.12, we have AB = BC, M is the mid-point of AB and N is the mid- point of BC. By using Euclid’s axiom, it is shown that AM = NC

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