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A triangle have three edges and three vertices. A triangle is a basic shape in geometry.

In this chapter we will cover the following topics related to triangle.

-Similar figures

A similar figures have a same shape but a similar figures not have a same size. In geometry a two circle are similar, two squares are similar etc.

-Similarity of triangles

A similar triangle have two triangles are said to be similar if their corresponding angles are equal and their corresponding sides are proportional.

-Criteria for similarity of triangles

-Area of similar triangles

-Pythagoras

In a right triangle the square of the hypotenuse is equal to the sum of the square of the other two side.

Published 22-Jul-2017 Bilingual

- Definitions, examples, counter examples of similar triangles
- (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
- (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
- (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
- (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
- (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.
- (Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other.
- (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides.
- (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
- (Prove) In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the angles opposite to the first side is a right triangle.

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