 Hello and welcome to the session. In this session, we will discuss about the areas of similar triangles. We know that two triangles are similar if the ratio of the corresponding sides is the same. And also area is measured in square units. So we get a very important result which says the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Consider these two triangles, triangle ABC is similar to triangle PQR. Now the ratio of the areas of these two triangles that is area of triangle ABC upon area of triangle PQR is equal to the square of the ratio of the corresponding sides. Now discuss a very important result before discussing the Pythagoras theorem. The result says if a perpendicular is drawn from the vertex of the right triangle of a right triangle the hypotenuse then triangles on both sides of the perpendicular are similar to the whole triangle and to each other. Consider this right triangle ABC which is right angled at B. Now we draw a perpendicular from the vertex of this right angle. Then according to this result we have that the triangles on both sides of this perpendicular that is these two triangles are similar to each other and also to whole of the triangle. Now let's discuss the Pythagoras theorem. According to this theorem we have that in a right triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides. This is the right triangle right angle that B. AC is the hypotenuse and ABC are other two sides of this triangle. So according to the Pythagoras theorem we have that AC square hypotenuse square is equal to sum of the squares of the other two sides. That is AB square plus BC square. Next we discuss the converse of Pythagoras theorem. According to this we have in a triangle a square of is equal to the sum of the squares of the other two sides. Then the angle opposite the first side is a right angle. If you consider this triangle ABC and if it's given to us that AC square is equal to AB square plus BC square. Then we have the angle opposite the first side that is angle opposite the side AC that is this angle is a right angle. This is the converse of Pythagoras theorem. This completes the session. Hope you have understood all the four results that we have discussed above.