Question

In the adjoining figure,we have x and y are midpoints of AC and BC and AX= CY .show that AC=BC

Answer 1

since
X and Y are mid-point if AC and BC
therefore,
AX = CX = 1/2 AC
& BY = CY = 1/2 BC

AX = CY
1/2 AC = 1/2 BC
therefore,
AC = BC

Answer 2

Proved below.

Step-by-step explanation:

Given:

Let us take a Δ ABC in which x and y are midpoints of sides AC and BC respectively such that  AX = CY.

The figure is shown below.

It is given that x  is a midpoint of AC, we get

AX = CX

This further gives,  

AC = AX + CX

AC = AX + AX    (Since AX=CX)  

AC=2AX                     [1]

Also, we are given that y is a midpoint of BC, we get  

BY = CY

This further gives,  

BC =  BY+ CY  

BC = CY + CY    (Since BY=CY)  

BC = 2CY                    [2]

We are given that AX=CY.

Note that when equals are added to equals then whole are also equal.This gives,  

AX + AX = CY + CY        

2AX = 2CY            

AC = BC      [ From (1)  and (2) ]

Hence proved.