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ASSIGNMENT

PRESENTED BY

APARNA.A.L MATHEMATICS REG: 13973002

KUCTE KOLLAM

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NATURAL RESOURCES- CONGRUENCE, SIMILARITY

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SI: NO. CONTENT PAGE NO.

1 INTRODUCTION 4

2 CONTENT 5-8

3 CONCLUSION 9

4 REFERANCE 10

INDEX

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INTRODUCTION

Natural resources occur naturally within environments that exist relatively undisturbed by humanity, in a natural form. A natural resource is often characterized by amounts of biodiversity and geodiversity existent in various ecosystems. In geometry, two figures or

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objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other.

CONTENT In elementary geometry the word congruent is often used as follows. The word equal is often used in place of congruent for these objects.

Two line segments are congruent if they have the same length.

Two angles are congruent if they have the same measure.

Two circles are congruent if they have the same diameter

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If two objects are similar, each is congruent to the result of a uniform scaling of the other.

In this figuer they are congruent

Star fish

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Orange

Determining congruence of polygons For two polygons to be congruent, they must have an equal number of sides (and hence an equal number—the same number—of vertices). Two polygons with n sides are congruent if they each have numerically identical sequences (even if clockwise for one polygon and counterclockwise for the other) side-angle-side-angle-... for n sides and n angles.

Congruence of polygons can be established graphically as follows:

First, match and label the corresponding vertices of the two figures.

Second, draw a vector from one of the vertices of the one of the figures to the corresponding vertex of the other figure. Translate the first figure by this vector so that these two vertices match.

Third, rotate the translated figure about the matched vertex until one pair of corresponding sides matches.

Fourth, reflect the rotated figure about this matched side until the figures match.

If at anytime the step cannot be completed, the polygons are not congruent.

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Similarity Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other. For example, all circles are similar to each other, all squares are similar to each other, and all equilateral triangles are similar to each other. On the other hand, ellipses are not all similar to each other, rectangles are not all similar to each other, and isosceles triangles are not all similar to each other.

These are similar circle.

Orange

If two angles of a triangle have measures equal to the measures of two angles of another triangle, then the triangles are similar. Corresponding sides of similar

called similar if they both

have the same shape, or one has

same shape, or one has

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polygons are in proportion, and corresponding angles of similar polygons have the same measure.

Figures shown in the same color are similar

Conclusion

Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in size. Either object can be rescaled, repositioned, and reflected, so as to coincide precisely with the other object. If two objects are similar, each is congruent to the result of a uniform scaling of the other. Two geometrical objects are called similar if they

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both have the same Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other, or one has the same shape as the mirror image of the other.

REFERENCES

1. http://www.mathsisfun.com/congruence/similarity.html

2. http://en.wikipedia.org/wiki/Similarity3. http://en.wikipedia.org/wiki/congruence