Question

If Q is the midpoint of PR and R is the midpoint of QS,
where P, Q, R, S lie on a straight line, then prove that PQ = RS .​

Answer 1

Answer:

Step-by-step explanation:

Given, Q is the mid-point of PR.

⇒ PQ = QR ... (1)

Again, R is the mid-point of QS.

⇒ QR = RS ... (2)

Now, PS = PQ + QR + RS

⇒ PS = 3 QR [using (1) and (2)]

⇒ QR = 1/3 PS

On putting value of QR in (1), we get

PQ = 1/3 PS

Answer 2

Answer:

PQ = RS when Q is the midpoint of PR and R is the midpoint of QS. Please refer the explanation for the proof.

Step-by-step explanation:

It is given that P,Q, R, S lie on a straight line.

Q is the mid point of PR.

So we can say that PQ=QR

R is the mid point of QS.

We can say that QR=RS

This line will look as shown in the image below.

It is asked to prove that PQ=RS.

We know that, PQ = QR           .............(1)

                        QR = RS           ..............(2)

From equation (1) and equation (2) we can say that PQ = RS.

Thus, it is proved.

The point that is in the middle of the line joining two points is called mid-point.

A one-dimensional figure that extends endlessly in both directions and does not have a thickness is called a line.

To know more about mid-point go to the following link.

https://brainly.in/question/54394088

To know more about line go to the following link.

https://brainly.in/question/47092640

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