Show that the opposite sides of a parallelogram are equal.

The opposite angles of a parallelogram are equal.

Show that the points (3, -1, 2), (5, -2, -3), (-2, 4, 1) and (-4, 5, 6) form a parallelogram. [Hint : Opposite sides of parallelogram are equal.]

Say True or False :(a) Each angle of a rectangle is a right angle.(b) The opposite sides of a rectangle are equal in length.(c) The diagonals of a square are perpendicular to one another.(d) All the sides of a rhombus are of equal length.(e) All the sides of a parallelogram are of equal length.(f) The opposite sides of a trapezium are parallel.

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

X and Y are the mid-points of the opposite sides AB and DC of a parallelogram ABCD. Prove that squareAXCY is a parallelogram.

P and Q are the mid-point of the opposite sides AB and CD of a parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PQRS is a parallelogram.

Show that the segment joining the mid-points of a pair of opposite sides of a parallelogram, divides it into two equal parallelograms. GIVEN : A parallelogram A B C D,E and F are the mid-points of opposite sides A B and C D respectively. TO PROVE : a r(||^(gm)A E F D)=a r(||^(gm)E B C F) CONSTRCUTION : Join E Fdot

State True or False If two adjacent sides of a parallelogram are equal, it is a rhombus

Prove that the bisectors of opposite angles of a parallelogram are parallel.

The given figure shows parallelograms ABCD and APQR. Show that these parallelograms are equal in area. [Join B and R]