Question

in the given figure pq is parallel to ab and pr is parallel to ac prove that qr is parallel to bc

Answer 1

The signs in the picture says that,
BQ = QO
CR = RO

So I may use " Mid point Theorem ( of the triangle) "

Then, as Q and R are the mid points of the line BO and CO so,
QR || BC and
2 QR = BC

Answer 2

Answer:

Given: PQ ║ AB , PR ║ AC and P is Mid point of AO (from figure).

To Prove: QR ║ BC  

Proof,

We use Mid Point Theorem and Converse Mid Point Theorem.

Mid Point Theorem states that if a line is drawn from a mid point of a side of triangle to mid point of 2nd side of a triangle then it is parallel to 3rd side of triangle.

Converse Mid point Theorem states that if a line is drawn from a mid point of side and parallel to 2nd side then it bisect the 3rd side.

In Δ AOB,

PQ ║ AB ( given ) &

P is mid Point of AO ( given in figure )

So, By converse Mid point Theorem, we get

⇒ Q is Mid point of OB  

In Δ AOC,

PR ║ AC ( given ) &

P is Mid point of AO ( given in figure )

So, By Converse Mid Point Theorem, we get

⇒ R is Mid point of OC.

In Δ BOC

Q is Mid point of OB & R is Mid point of OC ( from above )

So, By Mid Point Theorem.

⇒ QR ║ BC

Hence Proved