...rf^g, then j where all the quantities are positive. 9. Prove that in every triangle the square on the side subtending an acute angle is less than the sum of the squares on the aides containing that angle by twice the rectangle contained by either of these sides, and the...

...produced to F, show that DH produced will cut BF at right angles. 8. In any triangle the square on the side subtending an acute angle is less than the sum of the squares on the sides containing the acute angle by twice the rectangle contained by one of these sides and...

...into three pairs of equal rectangles. Deduce that the square on one side falls short of the squares on the other sides by twice the rectangle contained by either of these and the projection of the other upon it. 2. Define similar figures. Show that two quadrilaterals may...