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**Hint**: In a triangle line joining the mid point of two sides is parallel to the third side OR a line passing through midpoint of a side and parallel to the other side goes through the mid point of the third side.

**:**

__Complete step-by-step answer__As given \[X\] is mid point of \[QR\] and \[XZ||PQ\] then \[Z\] is the midpoint of \[PR\].

Now again, as \[Z\] is the midpoint of \[PR\] and \[YZ||PX\]it can be concluded that \[Y\] is the midpoint of \[XR\].

Now we have \[X\] is mid point of \[QR\] hence \[XR=\dfrac{1}{2}QR\]

Now as \[Y\] is the midpoint of \[XR\] we have \[YR=\dfrac{1}{2}XR\].

$\Rightarrow$ Now using the above two relation we have \[YR=\dfrac{1}{2}\times \dfrac{1}{2}QR\]\[\Rightarrow YR=\dfrac{1}{4}QR\]

**Note**: Two theorems can be used to prove the above problem.

1.In a triangle line joining the mid point of two sides is parallel to the third side.

2. In a triangle if a line parallel to one side of the triangle and passing through the midpoint of another side will bisect the third side.

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