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1.	If a point C lies between two points A and B such that`A C=B C`, then prove that `A C=1/2A B`. Explain by drawing the figure.
Answer» C lies on l AC+BC=AB (4th axiom) AC+AC=AB 2 AC=AB AC=1/2 AB

2.	If A. B and C are three points on a line, and B lies between A and C then prove that `A B-B C=A C`.
Answer» (AB+BC) and AC-coincial with each other by euclids, 4^(th) axiom these two quantity are equal AB+BC=AC

3.	Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.
Answer» If a straight line falling on two other straight lines, making interior angles on some side which are less than two right angles, then the two straight lines. if produced indefinitely, then they meet on that side on which the angles are less than two `90^o`angles.

4.	the number of dimension,a surface hasA. 1B. 2C. 3D. 0
Answer» Correct Answer - B Boundaries of a solid are called surfaces. A surface (plane) has only length and breadth . So , it two dimensions.

5.	A pyramid is a solids figure, the base of which isA. only a triangleB. onley a squareC. only a rectangleD. any polygon
Answer» Correct Answer - B A Pyramid is a solid figure , the base of which is a triangle or square or some other polygon.

6.	The side faces of a pyarmid areA. trianglesB. squaresC. polygonsD. trapeziums
Answer» Correct Answer - A The side faces of a pyramid are always triangles.

7.	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.
Answer» Yes, these postulates contain any undefined terms. No, they follow from euclids postulates.

8.	The statements that are proved are called axioms.
Answer» Because the statements that are proved are called theorems.

9.	Read the following statements which are taken as axioms (i) If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal. (ii) If a transversal intersect two parallel lines, then alternate interior angles are equal. Is this system of axioms consistent ? Justify your answer.
Answer» A system of axiom is called consistent , if there is no statement which can be deduced from these axioms such that it contradicts any axiom. We know that , if a transversal intersects two parallel lines , the each pair of corresponding angles are equal , which is a theorem. So , Statement I is false and not an axiom. Also, we know that , if a transversal intersects two parallel lines, then each pair of alternate interior angles are equal . It is also a theorem . So , Statement II is true and axiom. Thus, in given statements, first is false and second is an axiom. Hence , given system of axioms is not consistent.

10.	Read the following two statements which are taken as axiom: (i) If two lines intersect each other , then the vertically opposite angles are not equal. (ii) If a ray stands on a line , then the sum of two adjacent angles, so formed is equal to `180^(@)`. Is this system of axioms consistent ? Justify your answer.
Answer» We know that , if two lines intersect each other, then the vertically opposite angles are equal. It is a theorem , So given Statement I is false and not an axiom. We know that , if a ray stands on a line, then the sum of two adjacent angles so formed is equal to `180^(@)` . It is an axiom . So given Statement II is true and an axiom. Thus, in given statements first is fales and second is an axiom . Hence , given system of axioms is consistent.

11.	The number of dimension ,a solid hasA. 1B. 2C. 3D. 0
Answer» Correct Answer - C A soild has shape, size , position and can be moved from one place to another .So, solid has three dimensions, e.g., Cuboid.

12.	Euclid stated that all right angles are equal to each other in the form ofA. an axiomB. a definitionC. a postulateD. a proof
Answer» Correct Answer - C Euclid ststed that all right angles are equal to each other in the form of a postulate.

13.	The edges of a surface are curves.
Answer» Because the edges of surfaces are lines.

14.	Euclidean geometry is valid only for curved surfaces.
Answer» Because Euclidean geometry is valid only for the figures in the plane but on the curved