- A6
- B7
- C20
- D10
Step-by-Step Solution
Two distinct lines meet in at most one point, so each pair of roads gives one crossing: the 4 roads give . The new road crosses each of the 4 old roads at a new point: .
Answer: D) 10
Four straight roads in Chandigarh are shown; no two are parallel and no three pass through one point. A fifth straight road is built that is not parallel to any of them and does not pass through any existing crossing. How many crossing points will there be in all?
Class 9Introduction to Euclid's GeometryGeometry — Foundations
Key idea: The five postulates of Euclid
**Postulate 1**: A straight line may be drawn from any one point to any other point.
**Postulate 2**: A terminated line (segment) can be produced indefinitely (extended).
**Postulate 3**: A circle can be drawn with any centre and any radius.
**Postulate 4**: All right angles are equal to one another.
**Postulate 5** (the famous one): If a straight line falling on two straight lines makes the interior angles on the same side together less than two right angles (180°), then the two lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.
These 5 statements are the seeds. Everything else in classical geometry grows from them.
**Postulate 2**: A terminated line (segment) can be produced indefinitely (extended).
**Postulate 3**: A circle can be drawn with any centre and any radius.
**Postulate 4**: All right angles are equal to one another.
**Postulate 5** (the famous one): If a straight line falling on two straight lines makes the interior angles on the same side together less than two right angles (180°), then the two lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.
These 5 statements are the seeds. Everything else in classical geometry grows from them.
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