Question

his maths genius solve this

Answer 1

Refer the attachment for figure,

Here we can see that in quadrilateral ABCQ, opposite sides are parallel.

If each pair of opposite sides are parallel in a quadrilateral, then it's a ||gm.

=> ABCQ is a ||gm

=> BC = AQ (opposite sides are equal in a parallelogram)

Similarly, opposite sides are parallel in figure PACB

=> PACB is a ||gm

=> BC = PA (opposite sides are equal in a ||gm)

We have derived that

BC = AQ
and also, BC = PA

So on adding them, we get

BC + BC = AQ + PA

now, AQ + PA = PQ

=> BC + BC = PQ

=> 2BC = PQ

=> BC = PQ/2

=> BC = 1/2 PQ

Hope it helps dear friend ☺️✌️

Answer 2

$\textbf{ \huge{ \underline{ Hello Mate! }}}$

Given : ABC is triangle where lines are drawn parallel to AB, BC and CA.

To prove : I think its shoud be BC = 1 / 2 QR rather than BC = 1 / 2 PQ.

Proof : Since AR || BC and BR || AC.

ACBR is a parallelogram.

Therefore, BC = AR ____(1)

Since AB || QC and BC || AQ.

ABCQ is parallelogram.

Therefore, BC = AQ ____(2)

From (1) and (2) we get,

AQ = AR ( i.e. A is mId point on QR )

Multiplying 2 from equation 2 we get

2BC = 2AQ

2BC = QR

BC = 1 / 2 QR

$\textbf{ \large{ Q.E.D }}$

$\textbf{ Have great future ahead! }$