In the adjacent figure, we have AC = XD, C and D are mid points of AB and XY respectively. Show that AB = XY.

In the adjacent figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC||PR. Show that BC || QR.

In the adjacent figure ABCD is a parallelogram P and Q are the midpoints of sides AB and DC respectively. Show that PBCQ is also a parallelogram.

In the given figure, A, B and C are points on OP, OQ and OR respectively such that AB||PQ" and "AC||PR . Show that BC||QR .

ABCD is a square. E, F, G and H are the mid points of AB, BC, CD and DA respectively. Such that AE = BF = CG = DH . Prove that EFGH is a square.

If in a triangle AB=a,AC=b and D,E are the mid-points of AB and AC respectively, then DE is equal to

In the adjacent figure DeltaABC, D is the midpoint of BC. DE_|_AB, DF_|_AC and DE = DF . Show that DeltaBED ~= Delta CFD .

In the adjacent figure the sides AB and AC of Delta ABC are produced to points E and D respectively. If bisectors BO and CO of angleCBE and angleBCD respectively meet at point O, then prove that angleBOC = 90^(@)-(1)/(2) angleBAC .

In the adjacent figure, AB || CD, ‘t’ is a transversal intersecting E and F respectively. If ∠2 : ∠1 = 5 : 4, find the measure of each marked angles.

In the given figure, sides AB and AC of triangle ABC are extended to points P and Q respectively. Also, angle PBC lt angle QCB . Show that AC gt AB

Three identical rods AB , CD and PQ are joined as shown. P and Q are mid points of AB and CD respectively. Ends A , B , C and D are maintained at 0^(@)C , 100^(@)C , 30^(@)C and 60^(@)C respectively. The direction of heat flow in PQ is