Question

In fig x and y are midpoints of AB and BC and AX=CY. show that AB = BC

Answer 1

Answer:

Proved.

AB = BC.

Step-by-step explanation:

Given :

◆ x and y are midpoints of AB and BC.

◆ AX = CY

To Show :

Show that AB = BC.

Solution :

X and Y are the midpoints of AB and BC.

⇒ A => AX  = CX.

⇒ AC  = AX + CX

⇒ 2AX

__________

⇒ BY = CY.

⇒ BC = BY + CY.

⇒ 2CY.

We know that :

Euclid's theorem :

Things which are equal to the same things are equal to each other.

But,

⇒ AX = CY.

⇒ 2AX = 2CY.

⇒ AC = BC.

Remember -

Things which are double of same things are equal to one other.

Answer 2

SOLUTION:-

Given:

In attachment a figure X & Y are midpoints of AB & BC respectively,

such that AX = CY

To prove:

Show that AB= BC.

Proof:

The figure is shown above in attachment.

It is given that X is the midpoint of AC,

It is given that X is the midpoint of AC,this gives AX= CX

This further gives,

AC= AX + CX

AC= AX + AX [since AX=CX]

AC= 2AX..............(1)

Also, we are given that Y is the midpoint of BC which gives,

BY= CY

This further gives,

BC= BY + CY

BC= CY + CY [since BY=CY]

BC= 2CY.............(2)

We are given that AX= CY.

Note:

When equals are added to equals then whole are also equal.

So,

AX + AX = CY + CY

2AX = 2CY

=) AC = BC [from (1) & (2)]

Hence proved.

Hope it helps ☺️