Published on November 1, 2007
This presentation is Created by …. Ms Rashmi Kathuria at… K.H.M.S. Ashok Vihar Delhi.
Our Aim is to learn the concept Of similarity in mathematics.
Contents Introduction of the topic. Examples Similarity in mathematics
Introduction of the topic.
Similarity in mathematics
Introduction : There are variety of objects around you. Some of these have same shape but not necessarily the same size. What do you call them? Want to know?
We call them.. SIMILAR
DAILY LIFE AND SIMILARITY Observe the leaves and petals of a flower . SIMILARITY Observe the feathers of two or more same birds.
SIMILAR OBJECTS They have same shape but not necessarily the same size
Observe these cats. They are similar.
Similarity & Mathematics Figures that have same shape but not necessarily the same size are called similar figures .
PLEASE NOTE ANY TWO LINE SEGMENTS ARE SIMILAR . A B C D ANY TWO CIRCLES ARE SIMILAR .
PLEASE NOTE ANY TWO SQUARES ARE SIMILAR. A B C D E F G H ANY TWO EQUILATERAL TRIANGLES ARE SIMILAR. A B C D E F
SIMILAR POLYGONS DEFINITION TWO POLYGONS ARE SAID TO BE SIMILAR TO EACH OTHER ,IF 1.their corresponding angles are equal. 2.the lenghts of their corresponding sides are proportional.
Example: A B C D E F G H Quad. ABCD is SIMILAR TO Quad. EFGH B = F C = G D = H ALSO AB/EF = BC/FG = CD/GH = DA/HE.
How to write ? F a polygon ABCDEF is similar to a polygon GHIJKL , then we write Poly ABCDEF ~ Poly GHIJKL Note: ~ stands for “ is similar to”.
Checking for Similarity Square and Rectangle. Consider a square ABCD A B C D and a rectangle PQRS. P Q R They are equiangular but their sides are not proportional . They are not similar. S
Checking for Similarity Two Hexagons. Consider a hexagon ABCDEF and another hexagon GHIJKL. They are equiangular, but their sides are not proportional. They are not similar. A B C D E F G H I J K L
Checking for Similarity Two Quadrilaterals. Consider a quadrilateral ABCD A B C D and another quadrilateral PQRS. P Q R S They have their corresponding sides proportional but their corresponding angles are not equal. They are not similar.
Checking for Similarity Two Equilateral Triangles. Consider an equilateral triangle ABC A B C and another equilateral triangle PQR . P Q R They have their corresponding sides proportional . Also their corresponding angles are equal. They are similar.
ADVANCED THOUGHT If one polygon is similar to a second polygon and ~ the second polygon is similar to the third polygon, then ~ the first polygon is similar to the third polygon. ~
I hope you have clearly understood the concept of similarity in daily life and in mathematics.
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