AD and BC are equal and perpendiculars to a line segment AB. Show that CD bisects AB.

In a quadrilateral ABCD, it is given that AB |\|CD and the diagonals AC and BD are perpendicular to each other. Show that AD.BC >= AB. CD .

Draw the perpendicular bisector of a given line segment AB and write justification.

AB is a line segment and line l is its perpendicular bisector. If a point P lies on l, show that P is equidistant from A and B.

AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that, (i) AD bisects BC (ii) AD bisects /_ A.

The median AD of a DeltaABC is perpendicular to AB, than tanA + 2tanB=

D is the midpoint of the side BC of Delta ABC . If P and Q are points o AB and on AC such that DP bisects angle BDA and DQ bisects angle ADC , then prove that PQ || BC

AB is a chord of the parabola y^2 = 4ax with its vertex at A. BC is drawn perpendicular to AB meeting the axis at C.The projecton of BC on the axis of the parabola is

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

In the figure given seg PA, seg QB, seg RC and seg SD are perpendicular to line AD. AB=60, BC=70, CD=80and PS=280, then find PQ, QR and RS.