In the adjoining figure, two points A and B lie on the same side of a line 'l'. C is the mid-point of AB. If AD `botlandBEbotl,` then prove that CD = CE.

In the following figure , AB = BC , AD bot BC and CE bot AB . prove that AD = CE

In the adjoining figure, DeltaABC is right angled at C and M is the mid-point of hypotenuse AB, If AC = 32 cm and BC = 60 cm, then find the length of CM.

In the adjoining figure, D is the mid-point of side AB of Delta ABC and P be any point on side BC. If CQ ||PD , then prove that: area of Delta BPQ = (1)/(2) xx " area of " Delta ABC

In the adjoining figure, D is the mid-point of BC. If BM and CN are perpendiculars from B and C respectively on AD and AD produced, then prove that BM = CN.

In the adjoining figure, common tangents AB and CD to two circles intersect at P. Prove that AB=CD.

In the adjoining figure, PQRS is a parallelogram. A and B are the mid-points of PQ of SR respectively. If PS= BR, then prove that quadrilateral ADBC is a reactangle.

{:("Column A","In the rectangular coordinate system shown, points A and E lie on the x-axis, and points B and D lie on the y-axis. Point C is the midpoint of the line AB and point F is the midpoint of the line DE", "Column B"),("The slope of the line AB",,"The slope of the line DE"):}

In the adjoining figure (i) AB=BC, M is the mid -point of AB and N is the mid- point of BC. Show that AM=NC. (ii) BM=BN,M is the mid- point of AB and N is the mid - point of BC. Show that AB=BC.

In the given figure, AB and CD are two equal chords of a circle, with centre O. If P is the mid-point of chord AB, Q is the mid-point of chord CD and anglePOQ = 150^(@) find angleAPQ

ABCD is a parallelogram E is mid-point of AB and DE bisects angle D. Prove that CE bisects angle C