In the adjoining figure, we have X and Y are the mid-points of AC and

1.	In the adjoining figure, we have X and Y are the mid-points of AC and BC and AX = CY. Show that AC = BC.
Answer» Given, X is the mid-point of AC AX = CX= ½ AC ⇒ 2AX =2CX = AC …(i) Y is the mid-point of BC. BY = CY = ½ BC ⇒ 2BY = 2CY= BC …(ii) According to the question, We also have, AX=CY …(iii) Applying the Euclid’s axiom, “Things which are double of the same things are equal to one another”. We get, From Eq. (iii), 2AX = 2CY Using Eqs. (i) and (ii), we get, AC=BC Hence Proved.

In the adjoining figure, we have X and Y are the mid-points of AC and BC and AX = CY. Show that AC = BC.

Answer»

Given, X is the mid-point of AC

AX = CX= ½ AC

⇒ 2AX =2CX = AC …(i)

Y is the mid-point of BC.

BY = CY = ½ BC

⇒ 2BY = 2CY= BC …(ii)

According to the question,

We also have,

AX=CY …(iii)

Applying the Euclid’s axiom,

“Things which are double of the same things are equal to one another”.

We get,

From Eq. (iii),

2AX = 2CY

Using Eqs. (i) and (ii), we get,

AC=BC

Hence Proved.

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In the adjoining figure, we have X and Y are the mid-points of AC and BC and AX = CY. Show that AC = BC.

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