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

Draw a right triangle and the perpendicular from the midpoint of the of the hypotenuse to the base Prove that in the large triangle the distances from the midpoint of the hypotenuse to all thevertices are equal. .

Draw a right triangle and the perpendicular from the midpoint of the of the hypotenuse to the base Prove that the circumcentre of a right triangle is the midpoint of its hypotenuse. .

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 large right triangle and the lengths of all three sides of the small right triangle.

Prove that the lengths of the perpendiculars from any point on the bisector of an angle to the sides are equal.

The perpendicular from the square comers of a right triangle cuts the opposite side into two parts of 2 and 3 cm length. Prove that if the perpendicular from the square corner of the right triangle divides the opposite sides into partsof length a and b and if the length of the perpendicular is h, then h^2= ab .

The perpendicular from the square corners of a right angle triangle cuts the opposite side into two parts of 2 and 3 cm length. Calculate the perpendicular sides of the large triangle.

In a right triangle one of the perpendicular sides is one less than 2 times the smaller side. Hypotenuse is one more than two times the smaller side. By taking the smaller side as 'x cm' write the algebraic expression for the other two-sides. Compute all the 3 sides of the right triangle

What is the hypotenuse of the right triangle with perpendicular sides sqrt2 centimeteres and sqrt3 centimeters? How much larger than the hypotenuse is the sum of the perpendicular sides?

In the picture below, the top vertex of a triangle is joined to the midpoint of the bottom side of the triangle and then the midpoint of this line is joined to the other two vertices. Prove that the areas of all four triangles obtained thus are equal to a fourth of the area of the whole triangle.