At two ends of a horizontal line, angles of equal size are drawn, and two points on the slanted lines are joined. Prove that the two slanted lines at the ends of the horizontal line are in the same ratio

At two ends of a horizontal line, angles of equal size are drawn, and two points on the slanted lines are joined. Prove that the parts of the horizontal line and parts of slanted lines are in the same ratio.

At two ends of a horizontal line, angles of equal size are drawn, and two points on the slanted lines are joined. Explain how a line of length 6 cm can be divided in the ratio 3:4

Prove that the tangents drawn to a circle at the two ends of a diameter are parallel.

Write the next two lines of the pattern above.

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.

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.

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

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.

The picutre on the right shows two circles centred on the same point and the line intersecting them.Prove that the parts of the line between the circles on either side are equal.