- Rational Numbers
- Addition of Rational Number
- Subtraction of Rational Number
- Multiplication of Rational Numbers
- Division of Rational Numbers
- Rational Numbers on a Number Line
- Inserting Rational Numbers Between Two Given Rational Numbers
- Method of Finding a Large Number of Rational Numbers Between Two Given Rational Numbers
Squares and Square Root
Cubes and Cube Roots
Playing with Numbers
Ratio and Proportion
Percent and Percentage
Profit, Loss and Discount
Direct and Inverse Variations
- Algebraic Expressions
- Degree of Polynomial
- Product , Factor and Coefficient
- Like and Unlike Terms
- Combining like Terms
- Multiplying Monomial by Monomials
- Multiplying a Monomial by a Polynomial
- Multiplying a Polynomial by a Polynomial
- Dividing a Monomial by a Monomial
- Dividing a Polynomial by a Monomial
- Dividing a Polynomial by a Polynomial
- Simplification of Expressions
Linear Equations in One Variable
Special Types of Quadrilaterals
- Introduction of Constructions
- Construction of an Angle
- To Construct an Angle Equal to Given Angle
- To Draw the Bisector of a Given Angle
- Construction of Angles of 60°,30°,90° and 45°
- Construction of Bisector of a Line
- Drawing the Perpendicular Bisector of a Line Segment
- Construction of Parallel Lines
- Constructing a Quadrilateral
- Construction of Parallelograms
- Construction of a Rectangle When Its Length and Breadth Are Given.
- Construction of Rhombus
- Construction of Square
- Concept of Reflection Symmetry
Representing 3-D in 2-D
Area of a Trapezium and a Polygon
Surface Area, Volume and Capacity
Data Handling (Statistics)
The perpendicular bisector of a line segment:
Fold a sheet of paper. Let `bar"AB"` be the fold. Place an ink-dot X, as shown, anywhere.
Find the image X' of X, with AB as the mirror line.
Let `bar"AB"` and `bar"XX’"` intersect at O.
This means that `bar"AB" "divides" bar"XX’"` into two parts of equal length.
`bar"AB" "bisects" bar"XX’" or bar"AB" "is a bisector of" bar"XX’"`.
Hence, `bar"AB" "is the perpendicular bisector of" bar"XX’"`.
Construction using ruler and compasses:
Step 1: Draw a line segment `bar"AB"` of any length.
Step 2: With A as the centre, using compasses, draw a circle. The radius of your circle should be more than half the length of `bar"AB"`.
Step 3: With the same radius and with B as centre, draw another circle using compasses. Let it cut the previous circle at C and D.
Step 4: Join `bar"CD". "It cuts" bar"AB"` at O.
Use your divider to verify that O is the midpoint of `bar"AB"`.
Therefore, `bar"CD" "is the perpendicular bisector of" bar"AB".`
Shaalaa.com | Perpendicular Bisector of the Line Segment
Draw a line segment AB = 5.5 cm. Mark a point P, such that PA = 6 cm and PB = 4.8 cm. From point P, draw a perpendicular to AB.
In each of the following, draw perpendicular through point P to the line segment AB :
Draw a line segment AB = 6.2 cm. Mark a point P in AB such that BP = 4 cm. Through point P draw perpendicular to AB.