Knowing Our Numbers
- Introduction to Knowing Our Numbers
- Comparing Numbers
- Compare Numbers in Ascending and Descending Order
- Compare Number by Forming Numbers from a Given Digits
- Compare Numbers by Shifting Digits
- Introducing a 5 Digit Number - 10,000
- Revisiting Place Value of Numbers
- Expansion Form of Numbers
- Introducing the Six Digit Number - 1,00,000
- Larger Number of Digits 7 and Above
- An Aid in Reading and Writing Large Numbers
- Using Commas in Indian and International Number System
- Round off and Estimation of Numbers
- To Estimate Sum Or Difference
- Estimating Products of Numbers
- Simplification of Expression by Using Brackets
- BODMAS - Rules for Simplifying an Expression
- Roman Numbers System and Its Application
- Concept for Natural Numbers
- Concept for Whole Numbers
- Successor and Predecessor of Whole Number
- Operation of Whole Numbers on Number Line
- Properties of Whole Numbers
- Closure Property of Whole Number
- Associativity Property of Whole Numbers
- Division by Zero
- Commutativity Property of Whole Number
- Distributivity Property of Whole Numbers
- Identity of Addition and Multiplication of Whole Numbers
- Patterns in Whole Numbers
Playing with Numbers
- Arranging the Objects in Rows and Columns
- Factors and Multiples
- Concept of Perfect Number
- Concept of Prime Numbers
- Concept of Co-prime Number
- Concept of Twin Prime Numbers
- Concept of Even and Odd Number
- Concept of Composite Number
- Concept of Sieve of Eratosthenes
- Tests for Divisibility of Numbers
- Divisibility by 10
- Divisibility by 5
- Divisibility by 2
- Divisibility by 3
- Divisibility by 6
- Divisibility by 4
- Divisibility by 8
- Divisibility by 9
- Divisibility by 11
- Common Factor
- Common Multiples
- Some More Divisibility Rules
- Prime Factorisation
- Highest Common Factor
- Lowest Common Multiple
Basic Geometrical Ideas
- Concept for Basic Geometrical Ideas (2 -d)
- Concept of Points
- Concept of Line
- Concept of Line Segment
- Concept of Ray
- Concept of Intersecting Lines
- Parallel Lines
- Concept of Curves
- Different Types of Curves - Closed Curve, Open Curve, Simple Curve.
- Concept of Polygons - Side, Vertex, Adjacent Sides, Adjacent Vertices and Diagonal
- Concept of Angle - Arms, Vertex, Interior and Exterior Region
- Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle
- Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
Understanding Elementary Shapes
- Introduction to Understanding Elementary Shapes
- Measuring Line Segments
- Concept of Angle - Arms, Vertex, Interior and Exterior Region
- Right, Straight, and Complete Angle by Direction and Clock
- Acute, Right, Obtuse, and Reflex angles
- Measuring Angles
- Perpendicular Line and Perpendicular Bisector
- Classification of Triangles (On the Basis of Sides, and of Angles)
- Equilateral Triangle
- Isosceles Triangles
- Scalene Triangle
- Acute Angled Triangle
- Obtuse Angled Triangle
- Right Angled Triangle
- Types of Quadrilaterals
- Properties of a Square
- Properties of Rectangle
- Properties of a Parallelogram
- Properties of Rhombus
- Properties of Trapezium
- Three Dimensional Shapes
- Concept of Prism
- Concept of Pyramid
- Concept of Decimal Numbers
- Place Value in the Context of Decimal Fraction
- Concept of Tenths, Hundredths and Thousandths in Decimal
- Representing Decimals on the Number Line
- Interconversion of Fraction and Decimal
- Comparing Decimal Numbers
- Using Decimal Number as Units
- Addition of Decimal Numbers
- Subtraction of Decimals Fraction
Ratio and Proportion
- Introduction to Practical Geometry
- Construction of a Circle When Its Radius is Known
- Construction of a Line Segment of a Given Length
- Constructing a Copy of a Given Line Segment
- Drawing a Perpendicular to a Line at a Point on the Line
- Drawing a Perpendicular to a Line Through a Point Not on It
- Drawing the Perpendicular Bisector of a Line Segment
- Constructing an Angle of a Given Measure
- Constructing a Copy of an Angle of Unknown Measure
- Constructing a Bisector of an Angle
- Angles of Special Measures - 30°, 45°, 60°, 90°, and 120°
- Method using ruler and compasses
- Method using a ruler and a set-square
- Method using a ruler and a protractor
Perpendicular to a line through a point on it:
- Given a line l drawn on a paper sheet and a point P lying on the line. It is easy to have perpendicular to l through P. We can simply fold the paper such that the lines on both sides of the fold overlap each other.
- Tracing paper or any transparent paper could be better for this activity. Let us take such a paper and draw any line l on it. Let us mark a point P anywhere on l.
- Fold the sheet such that l is reflected on itself; adjust the fold so that the crease passes through the marked point P. Open out; the crease is perpendicular to l.
A. Method using ruler and compasses:
As is the preferred practice in Geometry, the dropping of a perpendicular can be achieved through the “ruler-compasses” construction as follows :
Step 1: Given a point P on a line l.
Step 2: With P as a centre and a convenient radius, construct an arc intersecting the line l at two points A and B.
Step 3: With A and B as centers and a radius greater than APconstruct two arcs, which cut each other at Q.
Step 4: Join PQ. Then `bar"PQ"` is perpendicular to l.
We write `bar"PQ"` ⊥ l.
B. Method using a ruler and a set-square:
Step 1: A line l and a point P are given. Note that P is on line l.
Step 2: Place a ruler with one of its edges along l. Hold this firmly.
Step 3: Place a set-square with one of its edges along the already aligned edge of the ruler such that the right-angled corner is in contact with the ruler.
Step 4: Slide the set-square along the edge of the ruler until its right-angled corner coincides with P.
Step 5: Hold the set-square firmly in this position. Draw `bar"PQ"` along the edge of the set-square.
`bar"PQ"` is perpendicular to l.
C. Method using a ruler and a protractor:
- Draw line RS. Take point M anywhere on the line.
- In order to draw a perpendicular through M, place the centre of the protractor on point M, as shown.
- Mark a point N at the 90° mark on the protractor.
- Draw a line passing through points M and N.
- The line MN is perpendicular to line RS at M.
Line MN ⊥ line RS.
Shaalaa.com | Perpendicular to a Line Through Point on the Line
Draw line l. Take any point P on the line. Using a set square, draw a line perpendicular to line l at the point P.
Draw line CD. Take any point M on the line. Using a protractor, draw a line perpendicular to line CD at the point M.
The common properties in the two set-squares of a geometry box are that they have a ______ angle and they are of the shape of a ______.