Line-segment AB is parallel to another line-segment CD. O is the mid-point of AD.
Show that (i) `DeltaAOB ~= DeltaDOC` (ii) O is also the mid-point of BC.

Line AB and CD are intersecting at ‘O’, OA = OB and OD = OC. Show that (i) Delta AOD ~= DeltaBOC and (ii) AD || BC .

C is the midpoint of the line segment bar(AB) and O is any point outside AB, show that vec(OA)+vec(OB)=2vec(OC) .

Prove by the theorem of Thales that the third side of a triangle is parallel to the line segment obtained by joining the mid-points of any two sides of the triangle and is half in length of its third side.

Prove that the line segment joining the mid-point of two transverse sides of a trapezium is parallel to its parallel sides.

Find the mid point of the line segment joining the points (3, 0) and (-1, 4)

The centre of two circle are P and Q they intersect at the points A and B. The straight line parallel to the line segment PQ through the point A intersects the two circles at the point C and D Prove that CD = 2PQ

The position vectors of the points A and B are 2vec(a)+vec(b) " and " vec(a)-3vec(b) . If the point C divides the line-segment bar(AB) externally in the ratio 1:2, then find the position vector of the point C. Show also that A is the midpoint of the line-segment bar(CB) .

Prove that the line segment joining the mid-points of the lateral sides of any trapezium is parallel to any of its parallel sides.

If D is the mid point of side BC of a triangle ABCand AD is perpendicular to BC, then