In Question 4, point $C$ is called a mid-point of line segment $AB$. Prove that every line segment has one and only one mid-point.

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? (iv) radius of a circle

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? (v) square

In Fig. 5.10, if $AC = BD$, then prove that $AB = CD$.

Which of the following statements are true and which are false? Give reasons for your answers. (iv) If two circles are equal, then their radii are equal.

Which of the following statements are true and which are false? Give reasons for your answers. (iii) A terminated line can be produced indefinitely on both the sides.

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.

Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note that the question is not about the fifth postulate.)

Which of the following statements are true and which are false? Give reasons for your answers. (ii) There are an infinite number of lines which pass through two distinct points.

If a point $C$ lies between two points $A$ and $B$ such that $AC = BC$, then prove that $AC = \frac{1}{2}AB$. Explain by drawing the figure.

Which of the following statements are true and which are false? Give reasons for your answers. (v) In Fig. 5.9, if $AB = PQ$ and $PQ = XY$, then $AB = X

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.

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

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? (ii) perpendicular lines

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? (iii) line segment