In this picture the horizontal lines at the top and bottom are parallel. Prove that the yellow and red triangles are of the same area.

Prove that the two triangles shown below have the same area

In the picture on the right, the angles between the radii and the chords are equal.Prove that the chords are of the same length.

In the two pictures below, the squares are of the same size. Prove that the green regions are of the same area.

In the picture below, the top vertex of a triangle is joined to the midpoint of the opposite side and then the point dividing this line in the ratio 2:1 is joined to the other two vertices. Prove that the areas of all three triangles in the picture on the right are equal to a third of the area of the whole triangle

The picture shows two circles with the same centre and two triangles formed by joining the centre to the points of intersection of the circles with two radii of the larger circle. prove that these triangles are similar .

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.

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.

In the picture below, the top vertex of a triangle is joined to the midpont of the opposite side and then the point dividing this line in the ratio 2:1 is joined to the other two vertices: Prove that the areas of all three triangles in the picture on the are equal to a third of the area of the whole triangle.