Show that the line segment joining the mid-points of a pair of opposite sides of a parallelogram, divides it into two equal parallelogram.
Theorems on Area
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Show that the line segment joining the mid-points of a pair of opposite sides of a parallelogram, divides it into two equal parallelogram.

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Given, ABCD be a parallelogram in which P and Q are mid-points of AB and CD respectively. Let us construct DG ⊥ AB and let DG = h, where h is the altitude on side AB. Area of ||gm ABCD = base × height = AB × h Area of ||gm APQD = AP × h = × h ......(1) [Since P is the mid-point of AB] The perpendicular distance between two parallel lines is always same everywhere, DG = QR = h. Area of ||gm PBCQ = PB × h = × h ......(2) [Since P is the mid-point of AB] From (1) and (2) Area of ||gm APQD = Area of ||gm PBCQ. Hence proved, that the line segment joining the mid-points of a pair of opposite sides of a parallelogram divides it into two equal parallelograms.

Mathematics

Show that the line segment joining the mid-points of a pair of opposite sides of a parallelogram, divides it into two equal parallelogram.

Theorems on Area

Related Questions

Find area of rhombus, the lengths of whose diagonals are 18 cm and 24 cm respectively.

Find area of trapezium, whose parallel sides measure 10 cm and 8 cm respectively and the distance between these sides is 6 cm.

In the given figure, the area of ||gm ABCD is 90 cm². State giving reasons:
(i) ar (||gm ABEF)
(ii) ar (△ABD)
(iii) ar (△BEF)

In the given figure, the area of △ABC is 64 cm². State giving reasons:
(i) ar(||gm ABCD)
(ii) ar (rect. ABEF)

Mathematics

Show that the line segment joining the mid-points of a pair of opposite sides of a parallelogram, divides it into two equal parallelogram.

Theorems on Area

Related Questions

Find area of rhombus, the lengths of whose diagonals are 18 cm and 24 cm respectively.

Find area of trapezium, whose parallel sides measure 10 cm and 8 cm respectively and the distance between these sides is 6 cm.

In the given figure, the area of ||gm ABCD is 90 cm2. State giving reasons:(i) ar (||gm ABEF)(ii) ar (△ABD)(iii) ar (△BEF)

In the given figure, the area of △ABC is 64 cm2. State giving reasons:(i) ar(||gm ABCD)(ii) ar (rect. ABEF)

In the given figure, the area of ||gm ABCD is 90 cm². State giving reasons:
(i) ar (||gm ABEF)
(ii) ar (△ABD)
(iii) ar (△BEF)

In the given figure, the area of △ABC is 64 cm². State giving reasons:
(i) ar(||gm ABCD)
(ii) ar (rect. ABEF)