If a point C lies between two points A and B such that AC = BC, then prove that Ac = 1/2AB. Explain by drawing the figure.
Give a definition for parallel lines. Are there other terms that need to be defined first? What are they, and how might you define them?
Give a definition for radius of a circle. Are there other terms that need to be defined first? What are they, and how might you define them?
Consider two ‘postulates’ given below:-
(i) Given any two distinct points A and B, there exists a third point C which is in between A and B.
(ii) There exist at least three points that are not on the same line.
Do these postulates contain any undefined terms? Are these postulates consistent? Do they follow from Euclid’s postulates? Explain.
- Mathematics Textbook for Class 9