Page 3 - Worksheet-Euclid's Geometry Ch-5 (Introduction to Euclid's Geometry)

15. Read the following axioms. 3
(i) Things which are equal to the same thing are equal to one another.

(ii) If equals are added to equals, the wholes are equal.

(iii) Things which are double of the same things are equal to one another.
Check whether the given system of axioms is consistent or inconsistent.

16. Read the following statements which are taken as axioms. 3
(i) If a transversal intersects two parallel lines, then corresponding angles are
not necessarily equal.
(ii) If a transversal intersects two parallel lines, then alternate interior angles
are equal.
Is this system of axioms consistent? Justify your answer.

17. Read the following statements: 4
An equilateral triangle is a polygon made up of three-line segments out of
which two-line segments are equal to the third-one and all its angles are 60°
each.
Define the terms used in this definition which you feel necessary. Are there any
undefined terms in this? Can you justify that all sides and all angles are equal
in an equilateral triangle?

18. In the adjoining figure 4

(i) AB = BC, M is the mid-point of AB and N is the mid-point of BC. Show that
AM = NC.
(ii) BM = BN, M is the mid-point of AB and N is the mid-point of BC. Show that
AB = B

19. State the True/False and justify. 4
a. Euclidean geometry is valid only for curved surfaces.
b. The boundaries of the solids are curves.
c. The edges of a surface are curves.
d. The things which are double of the same thing are equal to one another.

20. (i) Look at the adjoining figure. Show that length AH > sum of lengths of AB +
BC+CD.

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