Pythagoras' theorem

Can you prove Pythagoras' Theorem using enlargements and scale factors?

Prove that for every right angled triangle which has sides with integer lengths: (1) the area of the triangle is even and (2) the length of one of the sides is divisible by 5.

Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.

How does the perimeter change when we fold this isosceles triangle in half?

ABCD is a rectangle and P, Q, R and S are moveable points on the edges dividing the edges in certain ratios. Strangely PQRS is always a cyclic quadrilateral and you can find the angles.

Prove that the shaded area of the semicircle is equal to the area of the inner circle.

If the altitude of an isosceles triangle is 8 units and the perimeter of the triangle is 32 units.... What is the area of the triangle?

Three squares are drawn on the sides of a triangle ABC. Their areas are respectively 18 000, 20 000 and 26 000 square centimetres. If the outer vertices of the squares are joined, three more triangular areas are enclosed. What is the area of this convex hexagon?

What is the perimeter of this unusually shaped polygon...

A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?