Chap 14 Perimeter and Area

Chap 14

Perimeter  and Area

Some Important facts:

1.    The area of a region can be comprise by seeing and by measuring.

2.    1 cm² is the area of square of 1 cm.

3.    Formulae:

(a)   (i)  Perimeter of rectangle

= 2 x length + 2 x breadth

= 2 x (length + breadth)

(ii) Length of rectangle

                            = 1 x perimeter – breadth

                               2

(iii) Breadth of rectangle =

= 1 x perimeter – breadth

                               2

 (b) (i)  Perimeter of square = 4 x side

   (ii) Side of square = 1 x perimeter

                                   4

   (iii) Area of square = (side)²

          (c)     (i) Area of rectangle = length x breadth

                   (ii) Length of rectangle =           area

                                                                          Breadth

                   (iii) Breadth of rectangle =         area

                                                                            length

Chap 13 Constructions

Chap 13

Constructions

Some Important facts:

1.    Constructions can be drawn with the help of ruler, a set-square, a protractor and compass.

2.    Circle is a closed plane figure consisting of all points of the plane which are at a constant distance from a fixed point. The fixed point is called the centre of the circle and the constant distance is called the radius of circle.

3.    A line-segment whose one end point is on the centre of circle and other is on the circle, is called radius of circle. So the length of all radii is same.

4.    All the radii of circle are equal.

5.    Diameter of a circle is a line segment passing through its centre and having its end points on the circle.

6.    Diameter = 2 x radius.

7.    The circle divides the plane into three parts – interior, exterior and circle itself.

8.    The circle together with its interior constitutes the circular region.

9.    Consider a circle with centre O. for every point P in the interior, OP<r, for every point Q in the exterior OQ>r and for every point R on the circle, OR = r.

10. A line segment joining two points on a circle is called a chord of   

  the circle.

11. Diameter is the longest chord of a circle.

12. Any two points on a circle divide it into two parts known as arcs of circle. The smaller part is called the minor arc and the larger part is called the major arc. If both parts are equal then each part is called a semi-circle.

13. Circles having same centers are called concentric circles. 

Chap 12 Triangles

Chap 12

Triangles

Some Important facts:

1.    A closed figure obtained by joining three non-collinear points is called a triangle. Symbol ‘∆’ is used to denote a triangle.

2.    A triangle has three sides, three angles and three vertices.

3.    Three sides and three angles of a triangle are called its six parts.

4.    Triangle divides the plane into three parts – interior, exterior and triangle itself.

5.    A triangle together with its interior constitutes the triangular region.

6.    The sum of three angles of a triangle is 180°.

7.    Any exterior angle of a triangle is equal to sum of its interior opposite angles.

8.    The sum of two sides of a triangle is greater than its third side.

9.    A triangle which has all the sides of different lengths is called a scalene triangle.

10. A triangle having two sides equal is called as isosceles triangle.                                    

11. A triangle having all its sides equal is called a equilateral triangle.                                                    

12. A triangle, all whose angles are acute is called an acute angled triangle.

13. A triangle, one of whose angles is a right angle, is called a right angled triangle.

14. A triangle, one of whose angles is an obtuse angle, is called an obtuse angled triangle.

Chap 11 Pairs of Lines and Transversal

Chap 11

Pairs of Lines and Transversal .

Some Important facts:

1.    A line which intersects two or more lines in a plane at distinct points is called a transversal to the given line.

2.    Pairs of lines which do not intersect on a plane are called parallel lines.

          

                                                                                           

3.    Distance between two transversal lines is zero.

4.    Distance between two parallel lines is equal in each place and it is equal to perpendicular distance between them.

5.    If a transversal line intersects two parallel lines in the same plane, then

(i)            Each pair of corresponding angles is equal.

(ii)          Each pair of alternate angles is equal.

(iii)         Interior angles on same sides of transversal line are supplementary.

6.    If a transversal line intersects two non-parallel lines, then nothing is right as above in (i), (ii) and (iii).

7.    If a transversal line intersects two lines, then that two lines will be parallel if one condition from the following will be fulfilled.

(i)            One pair of corresponding angles is equal.

(ii)          One pair of alternate interior angles is equal.

(iii)         One pair of angles on same side of transversal line is equal.

Chap 10 Angles

Chap 10

Angles

Some Important facts:

1.    Ray has one initial point (or end point) A and it extends in any one direction upto infinity AB and Ray BA are two different rays.

2.    Two rays, having one initial point and having opposite direction are known as opposite rays.

3.    An angle is formed by two rays with a common initial point. This common point is known as the vertex of the angle and the rays are called its arms or sides.

4.    One complete angle = 4 right angles = 360°

One straight angle = 2 right angles = 180°

One right angle = 90°

Zero angle = 0°,

0°<acute angle<90°

90°< obtuse angle<180°

180°<reflex angle<360°

5.    Two line segments or a line and a line segment or a ray and a line segment are said to be perpendicular to each other if the lines represented by them meet at right angles.

6.    Two angles in a plane are said to be adjacent angles if they have a common vertex, a common arm and the other arms on the opposite sides of the common arm.

7.    Two adjacent angles form a linear pair, if their non-common arms form a straight line.

8.    Two angles formed by two intersecting lines having no common arm are said to be vertically opposite angles. Also, vertically opposite angles are equal.

9.    Two angles whose sum is 90° form a pair of complementary angles and each angle of this pair is called the complement of the other.

10. Two angles whose sum is 180° are said to be supplementary angles and each of these two angles is called the supplementary of the other.

11. Infinitely many rays can be drawn with a given point as initial point.

12. A ray is completely known if its initial point and one more point on it are known the initial point of a ray and one more point on it are sufficient to represent it completely.

13. While naming a ray its initial point is written first.

Chap 9 Line Segments

Chap 9

Line Segments

Some Important facts:

1.    A line segment is a part of a line.

2.    A line segment has two end points, but line has no.

3.    One and only one line segment can made joining of two different points.

4.    Length of line segment AB is written as AB

5.    Line segment are measured in centimeters (cm).Length can be measured in kilometers (km), meters (m) or centimeters (cm) etc. 

Chap 8 Basic Geometrical Concept

Chap  8

Basic Geometrical Concept

Some Important facts:

1.    A point has an exact position. A point has no length and breadth.

2.    Line extends endlessly in both the directions.

                                                                                                L

3.    Plane is a  flat surface which extends infinitely in all directions.

4.    Through a given point in a plane, infinitely many lines can be drawn.

5.    We can draw only one line passing through two different points.

6.    If two lines intersect each other (or intersect on extending) then the lines are known as intersecting lines.

7.    If two lines do not intersect each other (as it is or after extending them in both directions) then the lines are known as parallel lines.

8.    In a plane three or more lines pass through the same point then the lines are known as concurrent lines. The point through which they pass is known as point of concurrence.

9.    Three or more than three points are known as collinear points if they lie on a straight line.

         L       .                 .                       .                      

                         A                    C                     B