In the adjacent figure, we have $A C = X D, C$ and $D$ are mid points of $A B$ and $X Y$ respectively. Show that $A B = X Y$

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Solution

Given $A B = 2 A C$ (C is midpoint of AB)

And $X Y = 2 X D$ (D is mid point of XY)

and $A C = X D$ (given)

therefore, $\frac{A B}{2} = \frac{X Y}{2}$

$∴ A B = X Y$

Since things which are half of the same things are equal to one another.

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In the adjacent figure, we have AC=XD,C and D are mid points of AB and XY respectively. Show that AB=XY

Given AB=2AC (C is midpoint of AB)And XY=2XD (D is mid point of XY)and AC=XD (given)therefore, AB2=XY2∴AB=XYSince things which are half of the same things are equal to one another.

In the adjacent figure, we have $A C = X D, C$ and $D$ are mid points of $A B$ and $X Y$ respectively. Show that $A B = X Y$

Given $A B = 2 A C$ (C is midpoint of AB)

And $X Y = 2 X D$ (D is mid point of XY)

and $A C = X D$ (given)

therefore, $\frac{A B}{2} = \frac{X Y}{2}$

$∴ A B = X Y$

Since things which are half of the same things are equal to one another.