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.
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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. .

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.

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.

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 .

In this picture,the mid pointsof the sides of the large triangle are joined to make a small triangle inside. Calculate the coordinates of the vertices of the large triangle.

The perpendicular from the square corners of a right angle triangle cuts the opposite side into two parts of 2 and 3 cm length.Prove that two small triangles cut by the perpendicular have the same angles.