Four right triangles with sides [i]a[/i], [i]b[/i], and hypotenuse [i]c[/i], are arranged to form square GHIJ. You may adjust the size of the triangles by moving point [i]G[/i] and their shape by moving point [i]Q[/i]. Answer questions 1 and 2 first before moving the slider.

(1) What type of quadrilateral is the white region? Justify your answer. [br][br](2) What is the area of the quadrilateral in (1)?[br][br](3) Move slider [i]R[/i] to the extreme right to show slider [i]T[/i]. Then, move slider [i]T[/i] to the extreme right. What type/s of quadrilateral are the two white regions? Justify your answer.[br][br]3.) What are the areas of the quadrilaterals in (3)?[br][br]4.) How does the area of the quadrilateral in (1) relate to the areas of the quadrilaterals in (3)? [br][br]5.) What equation can we form from the relationship in (4) in terms of a, b, and c?