“The knowledge of
which geometry aims is the knowledge of eternal”
Omar Khayyam was a Persian mathematician, astronomer and poet. As
a poet, his classic work Rubaiyat attained world fame.
Khayyam’s work is an effort to unify Algebra and Geometry
Khayyam’s work can be considered the first systematic study and the first exact
method of solving cubic equations. He accomplished this task using Geometry.
His efforts in trying to generalize the principles of Geometry provided by
Euclid, inspired many European mathematicians to the eventual discovery of
non-Euclidean Geometry. Khayyam was a perfect example of being a notable
scientist and a great poet, an achievement which many do not possess.
To recall congruent triangles and understand the definition of
To understand the properties and construction of similar triangles
and apply them to solve
To prove basic proportionality theorem, angle bisector theorem and
study their applications and study the construction of triangles under given
To prove Pythagoras theorem and study its applications.
To understand the concept of tangent to a circle and study
construction of tangent to circle.
To understand and apply concurrency theorems.
The study of Geometry is concerned with knowing properties of
various shapes and structures. Arithmetic and Geometry were considered to be
the two oldest branches of mathematics. Greeks held Geometry in high esteem and
used its properties to discuss various scientific principles which otherwise
would have been impossible. Eratosthenes used the similarity of circle to
determine the circumference of the Earth, distances of the moon and the sun from
the Earth, to a remarkable accuracy. Apart from these achievements, similarity
is used to find width of rivers, height of trees and much more.
In this chapter, we will be discussing the concepts mainly as
continuation of previous classes and discuss most important concepts like
Similar Triangles, Basic Proportionality Theorem, Angle Bisector Theorem, the
most prominent and widely acclaimed Pythagoras Theorem and much more. Ceva’s
Theorem and Menelaus Theorem is introduced for the first time. These two new
theorems generalize all concurrent theorems that we know. Overall, the study of
Geometry will create interest in the deep understanding of objects around us.
Geometry plays vital role in the field of Science, Engineering and
Architecture. We see many Geometrical patterns in nature. We are familiar with
triangles and many of their properties from earlier classes.