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  • 1. Solve each of the following question using appropriate Euclid’s axiom: In the Fig. 5.12: AB equal to BC, M is the mid-point of AB and N is the mid- point of BC. Show that AM equal to NC. ii)Solve each of the following question using appropriate

i) Solve using appropriate Euclid’s axiom: In Fig. 5.12: AB = BC, M is the mid-point of AB and N is the mid-point of BC. Show that AM = NC.

ii) Solve using appropriate Euclid’s axiom:  In Fig. 5.12: BM = BN, M is the mid-point of AB and N is the mid-point of BC. Show that AB = BC.

 

Answers (1)

i) Here AB = BC

If M is the midpoint of AB then

AM = MB = 0.5AB

If N is the midpoint of BC then

BN = NC = 0.5 BC

According to Euclid’s axiom, things which are halves of the same thing are equal. 

We have, AB = BC

Multiply both sides by 0.5

0.5 AB = 0.5 BC

AM = NC

Hence proved.

ii) Here, BM = BN

If M is the mid-point of AB then

AM = MB 

2AM = 2BM = AB

If N is the mid-point of BC then

BN = NC 

2BN = 2NC = BC

According to Euclid’s axiom, things which are double of the same thing are equal to one another.

Now, BM = BN

Multiply both sides by 2

2BM = 2BN

Hence,

AB = BC

Hence proved.

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