Prove that in any triangle, the outer angle at a vertex is equal to the sum of the inner arigles at the outer two vertices.

Draw a quadrilateral and mark any two outer angles. Is thére any relation between the sum of these two and the inner angles at the other two vertices?

Prove that any outer angle of a cyclic quadrilateral is equal to the inner angle at the opposite vertex.

Prove that any outer. angle of a cyclic quadrilateral is equal to the interior angle, at the opposite vertex.

Prove that in any parallelogram, the 'sum of the squares of all sides is equal to the sum of the squares of the diagonals'.

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.

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

Draw a circle and a triangle with one vertex at the center of the circle and the other two on the circle. Draw another triangle of the same area with all three vertices on the circle.