In the picture below, the lines parallel to each side of the blue triangle through the opposite vertex are drawn to make the big triangle. How many triangles in the picture have the same area as that of the blue triangle? How many of them have the same measures of the blue triangle?

In the picture below, the lines, parallel to side of triangle A B C through the оррosite vertex are drawn to make the triangle PQR. a) Draw this picture, Draw the lines BQ, CP and AR. b) The triangles. ABP, AQC and BRC have the same arẹa as that of triangle A B C. Why? c) Find another 4 triangles of same area as that of triangle A B C from the picture which you have drawn and write their names.

Prove that the two triangles shown below have the same area

We have seen how we can draw a series of right triangles as in the picture. What are the lengths of the sides of the tenth triangle? .

We have seen how we can draw a series of right triangles as in the picture. How mulch more is the perimeter of the 10^th triangle than the perimeter of the ninth triangle? .

The perpendicular from the square corners of a right angle triangle cuts the opposite side into two parts of 2 and 3 cm length.Prove that two small triangles cut by the perpendicular have the same angles.

In this picture,the mid pointsof the sides of the large triangle are joined to make a small triangle inside. Calculate the coordinates of the vertices of the large triangle.

In the picture below, two lines are drawn from the top vertex of a triangle to the bottom side: Prove that the ratio in which these lines divide the length of the bottom side is equal to the ratio of the area of the three smaller triangles in the picture.

The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3cm//sec . How fast is the area decreasing when the two equal sides are equal to the base?

In the picture below, the top vertex of a triangle is joined to the midpoint of the bottom side of the triangle and then the midpoint of this line is joined to the other two vertices. Prove that the areas of all four triangles obtained thus are equal to a fourth of the area of the whole triangle.