Draw any angle with vertex O. Take a point A on one of its arms and B on another such that OA = OB, Draw the perpendicular bisectors of O̅A and O̅B. Let them meet at P. Is PA = PB?

Let I be a line and P be a point not on I. Through P, draw a line m parallel to I. Now join P to any point Q on I. Choose any other point R on m. Through R, draw a line parllel to PQ. Let this meet I at S. What shape do the two sets of parallel lines enclose?

Draw figures for the following statement. “If the two arms of one angle are respectively perpendicular to the two arms of another angle then the two angles are either equal or supplementary”.

Line l is the bisector of an angle angleA and B is any point on li. BP and BQ are perpendicular forms B to the arms of angleA . Show that: triangleAPB ~= triangleAQB (ii) BP = BQ or B is equidisitant from the arms of angleA .

Let A, B be the centres of two circles of equal radii, draw them so that each one of them passes throught the centre of the other. Let them intersect at C and D. Examine whether AB and CD are at right angles.

Let A be one point of intersection of two intersecting circles with centres O and Qd . The tangents at A to the two circles meet the circles again at B and C respectively. Let the point P be located so that AOPQ is a parallelogram. Prove that P is the circumcentre of the triangle ABC.

To construct a triangle similar to a given triangle ABC with its sides (3^(th) )/(7) the corresponding sides of triangle ABC, first draw a ray BX such that CBX is an acute angle and X lies on the opposite side of A with respect to BC. Them, locate points B_1, B_2, B_3, ... on BX at equal distance and the next step is to join

Draw the perpendicular bisector of bar(XY) whose length is 10.3 cm. (a) Take any point P on the bisector drawn. Examine whether PX = PY.