# Introduction to Euclids Geometry

## Class 9 NCERT Maths

### NCERT

1   Which of the following statements are true and which are false? Give reasons for your answers.$\\$ (i) Only one line can pass through a single point.$\\$ (ii) There are an infinite number of lines which pass through two distinct points.$\\$ (iii) A terminated line can be produced indefinitely on both the sides.$\\$ (iv) If two circles are equal, then their radii are equal.$\\$ (v) In the following figure, if $AB = PQ$ and $PQ = XY$, then $AB = XY.$

##### Solution :

(i)False.$\\$ Since through a single point ‘P’ below, infinite number of lines can pass. In the following figure, it can be seen that there are infinite numbers of lines passing through a single point P.$\\$ (ii)False.$\\$ Since through two distinct points, only one line can pass. In the following figure, it can be seen that there is only one single line that can pass through two distinct points P and Q.$\\$ (iii)True.$\\$ A terminated line can be produced indefinitely on both the sides. Let AB be a terminated line. It can be seen that it can be produced indefinitely on both the sides.$\\$ (iv)True.$\\$ If two circles are equal, then their centre and circumference will coincide and hence, the radii will also be equal.$\\$ (v)True.$\\$ It is given that AB and XY are two terminated lines (Line Segments) and both are equal to a third line PQ.$\\$ Euclid’s first axiom states that things which are equal to the same thing are equal to one another. Therefore, the lines AB =PQ and PQ = XY, Hence AB = XY will be equal to each other.

2   Give a definition for each of the following terms. Are there other terms that need to be defined first? What are they, and how might you define them?$\\$ (i) Parallel lines$\\$ (ii) Perpendicular lines$\\$ (iii) Line segment$\\$ (iv) Radius of a circle$\\$ (v) Square