MATHEMATICS Textbook for Class IX>Chapter 5 - Introduction to Euclid's Geometry>EXERCISE>Q 3

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Consider two ‘postulates' given below:

(i) Given any two distinct point $A$ 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 postulates? Explain.

Important Questions on Introduction to Euclid's Geometry

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MATHEMATICS Textbook for Class IX>Chapter 5 - Introduction to Euclid's Geometry>EXERCISE>Q 3

Consider the ‘postulates' given below:
There exist at least three points that are not on the same line.
Do the postulates contain any undefined terms? Are these postulates consistent?
Does it follow from Euclid’s postulates? Explain.

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MATHEMATICS Textbook for Class IX>Chapter 5 - Introduction to Euclid's Geometry>EXERCISE>Q 4

If a point

C

lies between two points

A

and

B

such that

A C = B C,

then prove that

A C = \frac{1}{2} A B

. Explain by drawing the figure.

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MATHEMATICS Textbook for Class IX>Chapter 5 - Introduction to Euclid's Geometry>EXERCISE>Q 5

Point

C

is called a mid-point of line segment

A B

, prove that every line segment has one and only one mid-point.

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MATHEMATICS Textbook for Class IX>Chapter 5 - Introduction to Euclid's Geometry>EXERCISE>Q 6

In the following figure, if $A C = B D,$ then prove that $A B = C D .$

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MATHEMATICS Textbook for Class IX>Chapter 5 - Introduction to Euclid's Geometry>EXERCISE>Q 7

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.)