R s aggarwal solutions mathematics class 9 Solutions for Chapter 6 introduction to euclids geometry

What is the difference between a theorem and an axiom?

Which of the following statements are true?

(i) A line segment has no definite length.

(ii) A ray has no end point.

(iii) A line has a definite length.

(iv) A line

(v) A ray

(vi) Two distinct points always determine a unique line.

(vii) Three lines are concurrent if they have a common point.

(viii) Two distinct lines cannot have more than one point in common.

(ix) Two intersecting lines cannot be both parallel to the same line.

(x) Open half-line is the same thing as ray.

(xi) Two lines may intersect in two points.

(xii) Two lines are parallel only when they have no point in common.

In the given figure, L and M are the mid-points of AB and BC respectively.

(i) If AB = BC, prove that AL = MC.

(ii) If BL = BM, prove that AB = BC.