Junior High School Mathematics Volume 2 (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1919 Excerpt: ...4. THE PYTHAGOREAN THEOREM A right triangle is a triangle of which one angle is a right angle. The side opposite the right angle is called the hypotenuse, and the other sides are called the legs. By drawing a right triangle whose legs are 3 in. and 4 in., respectively, it will be seen that the hypotenuse is just 5 in., and that the area of the square on the hypotenuse equals the sum of the areas of the squares on the two legs. This important truth was proved by Pythagoras, about 500 B.c., to be true of any right triangle. That is, The square on the hypotenuse of any right triangle is equal to the sum of the squares on the other two sides. Note.--Carpenters make use of this fact in laying out the foundation of a building when they want the walls at right angles to each other. Starting at one corner, a line 8 ft. long is taken in one direction along which the foundation is to be laid. Starting from the same corner, another line 6 ft. long is fastened to the end of the first line and moved about until a 10-ft. rod will just reach the outer extremities of the two lines. The truth of the Pythagorean theorem may be seen by drawing, or cutting from cardboard, figures like the following: B Let ABC be the right triangle. The square on the hypotenuse AC is equal to the four triangles, 1, 2, 3, and 4, and the small square, 5. Now put 1 and 2 in the position of the figure at the right, and the figure is equal to a square on AB and one on CB. 1. One leg of a triangle is 48 ft. and the other is 36 ft. What is the hypotenuse? 2. The hypotenuse of a right triangle is 85 ft. and one leg is 51 ft. What is the other leg? 3. One leg of a right triangle is 76 ft. and the hypotenuse is 95 ft. What is the other leg? 4. What is the diagonal (distance between the opposite corners) ...