## Pre-Requisires

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**Basic Geometrical Ideas | Speed Notes**

**Notes For Quick Recap**

A point determines a location. It is usually denoted by a capital letter.

A line segment corresponds to the shortest distancebetween two points. **(Scroll down to continue …)**

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The line

Two distinct lines meeting at a point are called **intersecting lines**.

Two lines in a plane are said to be **parallel** if they do not meet.

A ray is a portion of line starting at a point and going in one direction endlessly.

Any drawing (straight or non-straight) done without liftingthe pencil may be called a **curve**.

In this sense, a line is also a curve.

A simple curve is one that does not cross itself.

A curve is said to be closed if its ends are joined; otherwise it is said to be open. A polygon is a simple closed curve made up of line segments.

Here:

**(i) **The line segments are the sides of the polygon.

**(ii) **Any two sides with a common end point are adjacent sides.

**(iii) **The meeting point of a pair of sides is called a **vertex**.

**(iv) **The end pointsof the same side are **adjacent vertices**.

**(v) **The join of any two non-adjacent verticesis a **diagonal.**

An **angle **is made up of two rays starting from a common end point.

**A point** determines a location. A point is denoted by a capital letter.

A line segment corresponds to the shortest distance between two points. The line

Two distinct lines meeting at a point are called **intersecting lines**.

Two lines in a plane are said to be **parallel** if they do not meet.

A ray is a portionof line starting at a point and goingin one direction endlessly.

Any drawing (straight or non-straight) done without lifting the pencil may be calleda **curve**. In this sense, **a line is also a curve.**

A simple curve is one that does not cross itself.

A curve is said to be **closed** if its ends are joined; otherwise it is said to be **open**.

A polygon is a simpleclosed curve made up of line segments.

Here,

**(i) **The line segments are the sides of the polygon.

**(ii) **Any two sides with a common end point are **adjacent sides**.

**(iii) **The meeting point of a pair of sides is called a **vertex**.

**(iv) **The end pointsof the same side are **adjacent vertices**.

**(v) **The join of any two non-adjacent verticesis a **diagonal**.

An **angle **is made up of two rays startingfrom a **common end point**.

An angle leads to three divisions of a region:

**On the angle**, the **interior of the angle **and the **exterior of the angle**.

A **triangle** is a three-sided polygon.

A **quadrilateral **is a four-sided polygon. (It shouldbe named cyclically).

In any

similar relations exist for the other three angles.

A **circle** is the path of a point moving at the same distance from a fixed point.

The fixed point is the **Centre,** the fixed distanceis the **radius** and the distance around the circleis the** circumference.**

**A chord **of a circle is a line segment joining any two points on the circle.

A **diameter** is a chord passing throughthe Centre of the circle.

A sectoris the region in the interior of a circle enclosed by an arc on one side and a pair of radii on the other two sides.

A segmentof a circle is a region in the interior of the circle enclosed by an arc and a chord.

The diameter of a circle divides it into two semi-circles.

An angle leadsto three divisions of a region:

On the angle, the interior of the angle and the exterior of the angle.

The diameter of a circle divides it into two semi-circles.

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