Question

ABCD is a quadrilateral. P,Q,R and S are the points on the sides AB, BC, CD and
DA respectively such that AP:PB=AS:SD=CQ:QB-CR:RD. Prove that PQRS is a
parallelogram​

Answer 1

Answer:

ABCD is a quadrilateral P, Q, R, S are the points of trisection of the sides AB, CB, CD and AD respectively. Prove that PQRS is a parallelogram. ABCD is a quadrilateral in which P, Q, R, S are the points of trisection of the sides AB, CB, CD and AD respectively. ... Hence, PQRS is a parallelogram.

Step-by-step explanation:

Given: ABCD is quadrilateral where P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively

1 To prove: SRAC and LRAC

Proof:

In AADC,

Sand Rare the mid-points of sides AD and CD respectively.

:: SR || AC and SR =AC (Line segments joining the mid-points of two sides of a triangle is parallel to the third side and is half of it)