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

**Solution:**

The figure represents two line segments AB and BC.

Given, BM = BN ------------------- (1)

M is the midpoint of AB

N is the midpoint of BC

We have to show that AB = BC

Since M is the midpoint of AB we get

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

Since N is the midpoint of BC, we get

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

By using Euclid’s axiom,

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

Using (1) in (2) and (3),

2BM = 2BN

AB = BC

Therefore, AB = BC

**✦ Try This: **The coordinates of three consecutive vertices of a parallelogram are (1,3),(−1,2) and (2,5). The coordinates of the fourth vertex are

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

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

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

**Summary:**

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

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