1. This presentation is Created by …. Ms Rashmi Kathuria at… K.H.M.S. Ashok Vihar Delhi.
2. Our Aim is to learn the concept Of similarity in mathematics.
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4. 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?
9. Similarity & Mathematics Figures that have same shape but not necessarily the same size are called similar figures .
10. PLEASE NOTE ANY TWO LINE SEGMENTS ARE SIMILAR . A B C D ANY TWO CIRCLES ARE SIMILAR .
11. 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
12. 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.
13. 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.
14. 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”.
15. 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
16. 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
17. 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.
18. 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.
19. 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. ~
20. I hope you have clearly understood the concept of similarity in daily life and in mathematics.