Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squarea of its diagonals.

Prove that the sum of the squares drawn on the sides of a square is equal to the sum of the squares drawn on its diagonals.

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of the bisectors of the corresponding angles of the triangles. [The end-points of the angular bisectors are on the opposite sides of the angles.]

Prove that in a right traiangle, the square of the hypotemuse is equal to the sum of the squares of the other two sides.

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding altitudes of the triangles.

Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

Prove that the ratio of the areas of two similar triangle is equal to the square of the ratio of their corresponding medians.

Prove that the sum of the measures of four angles of a quadrilateral is 360^@ .

The houses of a row are numbered consecuitively from 1 to 49.Show that there is avalue of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it.Find the value of x.

Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.