...right-angled triangle, SeC. QED Cor. If the square described upon one of the sides of a triangle, be equivalent to the sum of the squares described upon the other two sides, the angle contained by these twq sides is a right angle. ELEMENTS OF GEOMETRY. BOOK II. DEFINITIONS....

...we have « 2 =: b 2 + c 2 , that is — 7Vtc square described upon the hypothenuse of a right-angled triangle, is equivalent to the sum of the squares described upon the other two sides. 173. We may demonstrate this truth from the areas immediately, without referring the lines to numbers,...

...PROP. XLVIII. THEOR. Fig. 72. If the square described upon one side (AC] of a triangle (ABC) be equal to the sum of the squares described upon the other two sides (AB andBC), the angle (ABC) opposite to that side is a right angle. 1 i ) SchoL From the point B draw...

...its altitude by the line joining the middle points of the sides which are not parallel. 256. Theorem. The square described upon the hypothenuse of a right...of the squares described upon the other two sides. Demonstration. Let squares be constructed upon the three sides of the right triangle ABC (fig. 130),...

...shall contain a greater angle. 60.*If the square described upon one of the sides of a trinngle be equal to the sum of the squares described upon the other two sides of it, the angle contained by these two sides is a right angle. 61. If a straight line be divided into...

...altitude by the line joining the middle points of the sides which are not parallel. ' 256. Theorem. The square described upon the hypothenuse of a right...of the squares described upon the other two sides. Proof. Let squares be constructed upon the three sides of the right triangle ABC (fig. 130), right-angled...

...parts, are between the same parallels. 3. If the square described upon one side of a triangle be equal to the sum of the squares described upon the other two sides of it, the angle contained by these two sides is a light angle. SECTION Il. — 1. To divide a straight...

...right angles as the figure has sides. 2. If the square described upon one side of a triangle be equal to the sum of the squares described upon the other two sides of it, the angle contained bj these two sides is a right angle. 3. In every triangle the square of...

...right angles as the figure has sides. 2. If the square described upon one side of a triangle be equal to the sum of the squares described upon the other two sides of it, the angle contained by these two sides is a right angle. 3. In every triangle the square of...

...proposition is also true, viz. that ' if the square described upon one of the sides of a triangle be equal to the sum of the squares described upon the other two sides of it, the angle between these two sides is a right angle.' Let ABC be a triangle, such that square...