P is a point equidistant from two lines `l` and `m` intersecting at point A (see Fig.
). Show that the line AP bisects `angleBAC`.

P is a point equidistant from two lines l and m intersecting at point A (see Fig. 7.38). Show that the line AP bisects the angle between them.

AB is a line-segment. P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (see Fig. 7.37). Show that the line PQ is the perpendicular bisector of AB.

The locus of a point equidistant from two points with position vectors veca and vecb is

AD and BC are equal perpendiculars to a line segment AB (see Fig. 7.18). Show that CD bisects AB.

How many points can be two distinct lines intersect at the most?

Two parallel lines l and m are intersected by a transversal p (see Fig. 8.15). Show that the quadrilateral formed by the bisectors of interior angles is a rectangle.

l and m are two parallel line intersects by another point of parallel lines p and q show that triangle ABC equiv triangleCDA

If a transversal intersects three lines than number of intersecting points will be :

If lines l and m intersect at a point Also m and n intersect at a point, is it necessary that lines l,m,n intersect at the same point.

Line l is the bisector of an angle angle A and B is any point on l. BP and BQ are perpendiculars from B to the arms of angle A (see Fig. 7.20). Show that: (i) triangle APB cong triangle AQB (ii) BP = BQ or B is equidistant from the arms of angle A .