Topics
Basic Concepts in Geometry
Angles
Integers
Operations on Fractions
- Concept of Fractions
- Conversion Between Improper Fractions and Mixed Numbers
- Addition of Fraction
- Subtraction of Fraction
- Fraction on the Number Line
- Multiplication of Fraction
- Concept of Reciprocal or Multiplicative Inverse
- Division of Fractions
Decimal Fractions
Bar Graphs
Symmetry
Divisibility
HCF-LCM
Equations
Ratio and Proportion
Percentage
Profit –Loss
Banks and Simple Interest
Triangles and Their Properties
Quadrilaterals
Geometrical Constructions
- Perpendicular Lines
- Drawing a Perpendicular to a Line at a Point on the Line
- Drawing a perpendicular to a line from a point outside the line
- The Perpendicular Bisector
- Drawing the perpendicular bisector of a segment using a compass.
- Carl Gauss’s Clever Trick
Three Dimensional Shapes
Construct an angle equal in measure to a given angle, using a compass and ruler.
To Construct an angle PQR equal in measure to a given angle ABC, using a compass and ruler.
1. Draw ray QR.
2. Place the compass point at vertex B of ∠ABC and, taking a convenient distance, draw an arc to cut the rays BA and BC at points D and E, respectively.
3. Using the same distance again, place the compass point at point Q of ray QR and draw an arc. Let this arc cut the ray QR at T.
4. Now place the point of the compass at point E and open the compass to a distance equal to DE.
5. Now, align the compass point with point T.
6. Using the distance equal to DE, draw an arc to cut the previous arc at S.
7. Draw the ray QS. Take any point P on ray QS.
8. Using a protractor, verify that the ∠PQR so formed is of the same measure as ∠ABC.
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