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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