Exercise Problem XIII — task. Mathematics CBSE, Class 9.

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$ABC$ is a triangle right angled at

$C$ . A line through the mid-point

$M$ of hypotenuse

$AB$ and parallel to

$BC$ intersects

$AC$ at

$D$ .

Show that

(i)

$D$ is the mid-point of

$AC$

(ii)

$MD ⊥ AC$

(iii)

$CM = MA = \frac{1}{2}AB$

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Important!

The line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side.

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19. Exercise Problem XIII