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#### Question

Give a definition for parallel lines. Are there other terms that need to be defined first? What are they, and how might you define them?

#### Solution

#### Similar questions

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.

Give a definition for perpendicular lines. Are there other terms that need to be defined first? What are they, and how might you define them?

If a point C lies between two points A and B such that AC = BC, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.

In the following figure, if AC = BD, then prove that AB = CD.

Give a definition for square. Are there other terms that need to be defined first? What are they, and how might you define them?