Important Points to remember about Maths:
Greek word "Mathema",which means "Science". So, Mathematics is the science of reasoning.The subject "Mathematics" is actually a group of many sciences so it's name ends at "s".
1. {Basic Arithmetic Signs} :- (+ , - , ÷ , ×)
2. Axiom :- An Axiom is a self evident truth.It is a true assumption common to all sciences. e.g.
- The whole is greater than any one of it's parts.
- The whole is the sum of it's parts.
- Things which are equal to the same thing are also equal to one another.
3. Pastulate:- It is simple fact that may be assumed to be true for a particular science. e.g.
- One and only one straight line can be drawn through two distinct points.
- All straight angles are equal to one another.
4. Theorem :- It is a statement that needs proof.It can be prove by a chain of reasoning in which certain axioms are assumed.
e.g.
(Hypotenuse)²= (Base)² +(Perpendicular)²
(Hypotenuse)²= (Base)² +(Perpendicular)²
(H)²= (B)² + (P)² or
(B)²= (H)² - (P)² or
(P)²= (H)² - (B)²
6. Planes:- A flat surface suggests a plane. e.g.
The Walls, The Floor of a room etc
7. Point :- A point is an idea. A point indicates a location or a position in space.We show it by a dot.We name a point by a Capital Letter.
e.g. .A , .B , .C etc
8. Line :- A Line is a straight row of points that goes on forever in both directions.
e.g. Line AB , Written
9. Line Segment:- A Line segment is a piece of a line with two end points.Line segment is suggested by a rope tied tightly between two poles or the iron bars of a window or the edges of a ruler.Line segment has two end points.
e.g. A and B .We write it as segment AB or ( AB ).It has a fixed length which can be measured with the help of a scale.
10. Straight Line:- If we extend a line segment on either ends, we get a line .It extends endlessly on either side.A line has no end points.We can also name a line by a single lower case letter such as ( l ) or ( m ).We cannot measure the length of a line. A line segment is the part of a line.
11. Ray :- A Ray is suggested by a Ray of light coming from a torch or The sun's rays.A Ray is a part of a line that has only one end point and extends endlessly only on one side marked by an arrow.We write it as : Ray AB or (
).
12. Angle :- An Angle is made up of two rays that have a common end point called the vertex. An Angle is the amount of turn from one position to another.
13. Difference among Straight line, Ray and Line Segment:
Strt.Line Ray L.Segment
It has no It has one It has two
end point. end point. end points.
Can be extended Can be extended Cannot be
on both sides on only one side. extended.
Length cannot Length cannot Length can
be measured. be measured. be measured.
14. Degrees :- A system used to measure angles in which a complete circle is 360 degrees, written 360°.
15. Idea of an Angle :- An Angle is formed when two Rays are drawn from the same end point. The end point is called the vertex of the angle. The two rays are called the arms or sides of the angle.
16. Kinds of an Angle :-
16. Radii :- Plural form of Radius.
17. Complete Revolution :- 360°
18. Diameter :- 2 × Radius
19. Complementary Angles :- Complementary Angles are two angles whose measure add up to 90°.
20. Supplementary Angles :-Supplementary Angles are two angles whose measure add up to 180°.
21. Congruent Angles :- Congruent Angles are angles that measure the same number of degrees.
6. Planes:- A flat surface suggests a plane. e.g.
The Walls, The Floor of a room etc
7. Point :- A point is an idea. A point indicates a location or a position in space.We show it by a dot.We name a point by a Capital Letter.
e.g. .A , .B , .C etc
8. Line :- A Line is a straight row of points that goes on forever in both directions.
e.g. Line AB , Written
9. Line Segment:- A Line segment is a piece of a line with two end points.Line segment is suggested by a rope tied tightly between two poles or the iron bars of a window or the edges of a ruler.Line segment has two end points.
e.g. A and B .We write it as segment AB or ( AB ).It has a fixed length which can be measured with the help of a scale.
10. Straight Line:- If we extend a line segment on either ends, we get a line .It extends endlessly on either side.A line has no end points.We can also name a line by a single lower case letter such as ( l ) or ( m ).We cannot measure the length of a line. A line segment is the part of a line.
11. Ray :- A Ray is suggested by a Ray of light coming from a torch or The sun's rays.A Ray is a part of a line that has only one end point and extends endlessly only on one side marked by an arrow.We write it as : Ray AB or (
).12. Angle :- An Angle is made up of two rays that have a common end point called the vertex. An Angle is the amount of turn from one position to another.
13. Difference among Straight line, Ray and Line Segment:
Strt.Line Ray L.Segment
It has no It has one It has two
end point. end point. end points.
Can be extended Can be extended Cannot be
on both sides on only one side. extended.
Length cannot Length cannot Length can
be measured. be measured. be measured.
14. Degrees :- A system used to measure angles in which a complete circle is 360 degrees, written 360°.
15. Idea of an Angle :- An Angle is formed when two Rays are drawn from the same end point. The end point is called the vertex of the angle. The two rays are called the arms or sides of the angle.
16. Kinds of an Angle :-
- Right Angle :- A Right Angle is an Angle that measures exactly 90°.
- Acute Angle :- An Acute Angle is an Angle that measures less than 90°.
- Obtuse Angle :- An Obtuse Angle is an Angle that measures more than 90° but less than 180°.
- Straight Angle :- A straight Angle is an angle that measures 180°; it's sides form a straight line.
- Reflex Angle :- A Reflex Angle is an Angle whose measure is greater than 180°.
16. Radii :- Plural form of Radius.
17. Complete Revolution :- 360°
18. Diameter :- 2 × Radius
19. Complementary Angles :- Complementary Angles are two angles whose measure add up to 90°.
20. Supplementary Angles :-Supplementary Angles are two angles whose measure add up to 180°.
21. Congruent Angles :- Congruent Angles are angles that measure the same number of degrees.
22. Vertical Angles :- Vertical angles are two non adjacent congruent Angles formed by intersecting lines.
23. Intersecting Lines :- Intersecting lines cross or merge.
24. Perpendicular Lines :-Perpendicular lines are two lines that intersect to form a right Angle.
25. Parallel Lines :- Parallel Lines are two lines in the same plane that never intersect.
26. Chord :- A chord is a segment which isn't passing through the center of a circle but touching with it's end points.
27. Circumference :- The circle is a closed curve.Its total length starting from a point going round and coming back to the same point, is called the Circumference.
28. Ratio of a Circle:
Circumference/Diameter = 22/7
If (r) is the radius,Then
Diameter = 2r
Circumference = 22/7 (Diameter)
= 22/7 (2r)
Diameter = Circumference * 7/22
29. Triangle :- A Triangle is a plane figure formed by three segments having common end points when taken in pairs or a figure having three sides, "Tri" means three because a triangle has three angles.
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23. Intersecting Lines :- Intersecting lines cross or merge.
24. Perpendicular Lines :-Perpendicular lines are two lines that intersect to form a right Angle.
25. Parallel Lines :- Parallel Lines are two lines in the same plane that never intersect.
26. Chord :- A chord is a segment which isn't passing through the center of a circle but touching with it's end points.
27. Circumference :- The circle is a closed curve.Its total length starting from a point going round and coming back to the same point, is called the Circumference.
28. Ratio of a Circle:
Circumference/Diameter = 22/7
If (r) is the radius,Then
Diameter = 2r
Circumference = 22/7 (Diameter)
= 22/7 (2r)
Diameter = Circumference * 7/22
29. Triangle :- A Triangle is a plane figure formed by three segments having common end points when taken in pairs or a figure having three sides, "Tri" means three because a triangle has three angles.
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