# 6. Triangles

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**Download Free NCERT Solutions Class 10th Science Chapter 6 Triangles**

Definitions, examples, counter examples of similar triangles.

1. **(Prove)** If a line is drawn parallel to one side of a triangle to intersect the other two sides indistinct points, the other two sides are divided in the same ratio.

2. **(Motivate)** If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.

3. **(Motivate)** If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.

4. **(Motivate)** If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.

5. **(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.

6. **(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.

7. **(Prove)** The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides.

8. **(Prove)** In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.

9. **(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 angle.