Introduction to Euclid's Geometry

Topics in this chapter

• Euclidean Geometry Foundations
• Geometric Objects and Definitions
• Axioms and Common Notions
• Euclid’s Postulates
• Geometric Constructions and Reasoning
• Parallel Postulate and Non-Euclidean Geometry

Cheat sheet

Practice questions

1. Question 1Q-3E9433

   Which of the following statements is a definition according to Euclid's elements rather than an axiom or postulate?

   1. A.A point is that which has no part.
   2. B.Things which are equal to the same thing are equal to one another.
   3. C.If equals be added to equals, the wholes are equal.
   4. D.All right angles are equal to one another.
   See the answer and solution
2. Question 2Q-540BAE

   How many lines can pass through a single given point?

   1. A.Only one
   2. B.Two
   3. C.Infinitely many
   4. D.Zero
   See the answer and solution
3. Question 3Q-E5FC21

   Given two distinct points in a plane, how many straight lines can be drawn passing through both points?

   1. A.One and only one
   2. B.Two
   3. C.Infinitely many
   4. D.None
   See the answer and solution
4. Question 4Q-C5F28F

   If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the angles are less than two right angles. This statement is known as:

   1. A.Euclid's First Postulate
   2. B.Euclid's Fifth Postulate
   3. C.Euclid's Axiom 5
   4. D.Playfair's Axiom
   See the answer and solution
5. Question 5Q-95D012

   Which of the following is a 'Common Notion' (Axiom) given by Euclid?

   1. A.A circle may be described with any centre and any radius.
   2. B.All right angles are equal to one another.
   3. C.The whole is greater than the part.
   4. D.Through a given point not on a line, exactly one parallel line can be drawn.
   See the answer and solution