Q17 of 109 Page 330

In the given figure, AC is a diagonal of quad. ABCD in which BL ⊥ AC and DM ⊥ AC. Prove that or (quad. ABCD)

Here we have ABCD as a quadrilateral with one of its diagonal as AC and BL and DM are perpendicular to AC

Thus, ar(ABCD) = ar(∆ADC) + ar(∆ABC)

Since, (BL ⊥ AC) and (DM ⊥ AC)

∴ Area of ABCD = ( ⨯ AC ⨯ BL) + ( ⨯ AC ⨯ DM)

= ⨯ AC ⨯ (BL + DM)

In the given figure, ABCD is a trapezium in which AB || DC and diagonals AC and BD intersect at O. Prove that ar(ΔAOD) = ar(ΔBOC).

Show that a diagonal divides a parallelogram into two triangles of equal area.

||gm ABCD and rectangle ABEF have the same base AB and are equal in areas. Show that the perimeter of the ||gm is greater than that of the rectangle.

In the adjoining figure, ABCD is a ||gm and E is the mid-point of side BC. If DE and AB when produced meet at F, prove that AF = 2AB.