Prove that the area of a triangle is invariant under the translation of the axes.

Prove that the slope of a line is invariant under the translation of the axes.

Statement 1 : The area of the triangle formed by the points A(1000 ,1002),B(1001 ,1004),C(1002 ,1003) is the same as the area formed by the point A^(prime)(0,0),B^(prime)(1,2),C^(prime)(2,1) Statement 2 : The area of the triangle is constant with respect to the translation of axes.

prove that The areas of the two similar triangles are in the ratio of the square of the corresponding medians.

If a triangle and a parallelogram are on the same base and between the same parallels, then prove that the area of the triangle is equal to half the area of the parallelogram.

prove that the area of a triangle is four times the area of the triangle formed by joining the mid-points of its sides.

Prove that the area of equilateral triangle described on the side of a square is half the area of the equilateral triangle described on its diagonal.

Prove that the area of equilateral triangle described on the side of a square is half the area of the equilateral triangle described on its diagonal.

Prove that the area of the equilateral triangle described on the side of a square is half the area of the equilateral triangle described on its diagonal.

Name two invariant points under reflection in the x-axis.

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.