Question

if a line is drawn parallel to one side of a triangle intersecting the other two side then it divides the two sides in the same ratio

Answer 1

Answer:

Given: ΔPQR, in which XY || QR, XY intersects PQ and PR at X and Y respectively.

To prove:

Construction: Join RX and QY and draw YN perpendicular to PQ and XM perpendicular to PR.

Proof:

Since, Area of a triangle =

Therefore, ar (ΔPXY) = …(1)

Also, ar (ΔPXY) = …(2)

Similarly, ar (ΔQXY) = …(3)

And, ar (ΔRXY) = …(4)

Dividing (1) by (3), we get

Again, dividing (2) by (4), we get

Since the area of triangles with same base and between same parallel lines are equal, so

(as and are on same base XY and between same parallel lines XY and QR)

Therefore, from (5), (6) and (7), we get

Hence, proved.

Step-by-step explanation: