Answer

Verified

438k+ views

**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.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

How do you graph the function fx 4x class 9 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Change the following sentences into negative and interrogative class 10 english CBSE