...loci. The 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, the...

...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* = AB* +...

...altitudes. 102. Use some of the following figures to establish the fact that the square on the hypothenuse of a right triangle equals the sum of the squares on the other sides. NOTE. — These figures have come from various sources, principally, however, from students...

...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 ....

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

...two or more of 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 much."...

...discovered the theorems that 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...

...discovered the theorems that 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...

...discovered the theorems that 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...

...J> 3. Remove the 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 lines...