...co-ordinates of A are x=7, у = — 4 ; the co-ordinates of B are x = 4, у = — 7. Since the square on the hypotenuse of a right triangle equals the sum of the squares on the other two sides, inspection of the diagram shows that (if r be the radius of the circle), Hence,...

...explained in Art. 260. Using this language, the Pythagorean proposition is often stated as follows: The square of the hypotenuse of a right triangle equals the sum of the squares of the other two sides. The proposition is often put in the form of an equation, thus: AC* = A Bz + B...

...of conseq.H I as any ant, is to its conseq. J PROPOSITION XI THE PYTHAGOREAN THEOREM 258. Theorem. The square of the hypotenuse of a right triangle equals the sum of the squares of the legs. First Method Appl. Prove AC * = AB * + B(f Cons. Draw -L BD Dem. AB = AC x AD .. , t . ....

...whose faces are triangular. Pythagorean theorem. The one first proved by Pythagoras, that the square on the hypotenuse of a right triangle equals the sum of the squares on the other two sides. Quadrilateral. A figure having four sides. Quantity. Answer to the query "How...

...the areas of similar polygons are as the squares of their homologous sides, and that the square on the hypotenuse of a right triangle equals the sum of the squares on the other two sides. The latter is called the Pythagorean theorem. They also discovered how to construct...

...the areas of similar polygons are as the squares of their homologous sides, and that the square on the hypotenuse of a right triangle equals the sum of the squares on the other two sides. The latter is called the Pythagorean theorem. They also discovered how to construct...

...the areas of similar polygons are as the squares of their homologous sides, and that the square on the hypotenuse of a right triangle equals the sum of the squares on the other two sides. The latter is called the Pythagorean theorem. They also discovered how to construct...

...geometrical construction the point corresponding to any rational number. Furthermore, by the principle that the square of the hypotenuse of a right triangle equals the sum of the squares of the other two sides, we can find the point corresponding to any irrational number expressed by square-root...

...the given line, it must be interpreted as in §329. (a) The Pythagorean proposition is often stated: The square of the hypotenuse of a right triangle equals the sum of the squares of the other two sides. It is frequently expressed as an algebraic equation, thus: A~C 2 = A~B 2 +"B~C...

...rectangles and triangles as shown in Fig. 79. Compare the remainders. This proves that — The square on the hypotenuse of a right triangle equals the sum of the squares on the other two sides. Arrange the figures as shown in fig. 80, and paste them in your book. The dotted...