Question

6. In the Fig.5.6, we have BX = ½ AB, BY = ½ BC and AB = BC. Show that BX = BY.

Answer 1

Answer:

Given,

(b) (i)

(u) Answer: (/u)

AB=BC -(İ)

And BX= 1/2 AB

And BY= 1/2 BC -(İİ)

By Ecuclids axion 7,

From (İ) and (İİ)

Therefore BX=BY

Answer 2

\__ Answer __/

Given :-

BX = ½ AB

BY = ½ BC

AB = BC

Required to prove :-

• BX = BY

Proof :-

Given :-

BX = ½ AB

BY = ½ BC

AB = BC

We need to prove that BX = BY

So,

Consider

AB = BC

Multiplying with ½ on both sides

½ ( AB ) = ½ ( BC )

½AB = ½BC

Since, it is given that ;

BX = ½ AB

BY = ½ BC

Hence,

BX = BY

Here we need to use euclid's axiom ;

The things which are halves of the same things are equal to one another )

Hence proved ✅

Additional Information :-

Euclid's axioms :-

1. If equals are subtracted from equals , the remainders are equal .

2. If equal are added to equals, the wholes are equal .

3. whole is greater than part .

4. Things which coincide with each other are equal to one another .

5. Things which are equal to same things are equal to one another .

6. Things which are double of same things are equal to one another .

These are the axioms given the Greek mathematician " Euclid "

These were been written in the Elements .

Elements means the books written by Euclid .

He had totally written 23 elements .

With axioms he also given some postulates too.