Question

If X and Y are respectively the mid-points of AB and BC and AX=CY, show that AB=BC.
(draw the mid-points X and Y for your convenience)​

Answer 1

Answer:

if AX=CY,THEN AB=BC as X&Y are at mid points of AB&BC

Answer 2

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$\huge\bold\red{{Given,}}$

☆ x and y are midpoints of AB and BC.

☆AX = CY

$\huge\bold\orange{{To -prove:-}}$

☆ AB = BC.

$\huge\bold\purple{{proof:-}}$

X and Y are the mid point of AB and BC

⇒ A ➪ AX = CX.

⇒ AC = AX + CX

⇒ 2AX

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⇒ BY = CY.

⇒ BC = BY + CY.

⇒ 2CY.

we know that things which are equal to the same things are equal to each other.

But,

⇒ AX = CY.

⇒ 2AX = 2CY.

⇒ AC = BC.

Hence proved-----------------

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