FORM 3, Chapter 1, 2 & 3

FORM 3

CHAPTER 1


1. A transversal is a straight line that intersects two or more straight lines.

2. A transversal intersecting a pair of lines results in eight angles. Four angles between the two lines are called interior angles and the other four angles are called exterior angles.

3. Corresponding angles are on the same side of a transversal and involve an interior angle and an exterior angle.


4. Alternate angles are interior angles on opposite sides of a transversal.

5. When a transversal intersects parallel lines, the corresponding angles are equal.

6. When two straight lines are cut by a transversal, the two lines are parallel if
- the corresponding angles are equal or

- the alternate angles are equal or

- the interior angles on the same side of the transversal are supplementary.



CHAPTER 2 = Polygons (ii)

1.A regular polygon is a polygon where all the sides are the same, and all the interior angles are the same.

2. If all the sides and all the angles of a polygon are not equal, the polygon is called an irregular polygon or a non-regular polygon.

3. If none of the interior angles of a polygon is a reflex angle, then the polygon is called a
convex polygon if one of the interior angles of a polygon is a reflex angle, then the polygon is called a concave polygon.

4. All regular polygons have many axes of symmetry.

5. The number of axes of symmetry is equal to the number of sides of the regular polygon.

Example

(a) An equilateral triangle has 3 axes of symmetry.


(b) A square has 4 axes of symmetry.


3. A polygon which is not a regular polygon may have axes of symmetry, but the number of

axes of symmetry is not equal to the number of sides (it is always less than the number of sides).


Example

(a) One axis of symmetry.

(b) One axis of symmetry.

(c) 2 axes of symmetry


4. A polygon can be divided into several triangles by drawing a line from one vertex to another non-adjacent vertex.


Examples

Quadrilateral

Number of sides : 4
Number of triangles: 4 - 2 = 2
Sum of interior angles = 2 x 180o = 360o


Pentagon

Number of sides: 5
Number of triangles: 5 - 2 = 3
Sum of interior angles = 3 x 180o = 540o


Hexagon

Number of sides: 6
Number of triangles: 6 - 2 = 4
Sum of interior angles = 4 x 180o = 720o


Polygon

Number of sides: n
Number of triangles: n - 2
Sum of interior angles = (n - 2) x 180o


6. The sum of interior angles of a polygon is the sum of angles of the triangles(which is 180o) multiplied by the number of triangles (which is two less than the number of sides)

7. The general formula for the sum of interior angles of a polygon with n sides is

8. All interior angles of a regular polygon are equal.

9. Since interior angle + exterior angle = 180o, therefore, all exterior angles of a regular polygon are equal.

10. The size of an interior angle of a regular polygon with n sides is equal to



CHAPTER 3 = Circles (II)


Definitions related to circles:

Arc: A continuous piece of a circle is called an arc. In other words, any portion of the circumference of a circle is called an arc.

Chord: A straight line joining any two points on the circumference of a circle is called a chord.

Circumference: The perimeter of a circle is called its circumference

Diameter: Any straight line drawn through the centre and terminating at both ways by the circumference is called a diameter.

Origin: Origin refers to the center of a circle

Pi ( ): An approximate value of is 22/7 which is correct to two decimal places. A more accurate value of is 3.14159 which is correct to five decimal places.

Radius: The constant distance of every point on the circle from its centre is called the radius of the circle. It is half of the diameter.

Sector: A sector is that part of a circle, which lies between an arc and two radii joining the extremities of the centre. The most important sector is a quadrant, which is one-fourth of the circle.

Tangent of a circle: It is a line perpendicular to the radius that touches only one point on the circle.

Circumference of a circle: = 2 r where is 22/7 or 3.14159




CYCLIC QUADRILATERALS

1. A cyclic quadrilateral is a quadrilateral with all its vertices lying on the circumference of the circle.


2. The sum of the interior opposite angles is 180 degrees.


3. The exterior angle of a cyclic quadrilateral is equal to its corresponding interior opposite angle.

( By : Ashvini Sekar & Juycintha Presha )