Draw a $8$ centimetres long line and divide it in the ratio $2:3$.

Draw an Equilateral triangle of perimeter $10$ centimeters.

Draw triangle of perimeter $10$ centimeters and sides in the ratio $3:4:5$.

Draw triangle of perimeter $10$ centimeters and sides in the ratio $2 : 3 : 4$.

In the picture below, the diagonals of the trapezium $ABCD$ intersect at $P$. Prove that $PA \times PD = PB \times PC$

In the picture, the perpendicular is drawn from the midpoint of the hypotenuse of a right triangle to the base. Calculate the length of the third side of the larger right triangle and the lengths of all three sides of smaller right triangle.

Draw a right triangle and the perpendicular from the midpoint of the hypotenuse to the base. Prove that this perpendicular is half the perpendicular side of the larger triangle.

Draw a right triangle. Prove that the perpendicular drawn from the midpoint of the hypotenuse to the base bisects the base of the triangle.