...• — -', it will become gin c = sin A cos H + sin it cos A, Now, since in every plane triangle, the sum of the three angles is equal to two right angles, A + B = supplement of c ; and, since an angle and its supplement have the same sine, it follows that...

...case the angle DEH and the angle BAC would together make two right angles. THEOREM. In. every triangle the sum of the three angles is equal to two right angles. , 41. Demonstration. Let ABC (Jig. 41) be any triangle; produce the side CA toward D, and draw to the...

...Note II. of his Geometry, gives of the fundamental proposition, that, in every rectilineal triangle, the sum of the three angles is equal to two right angles. This demonstration is the more remarkable, as it makes no use of the theory of parallels, but, on the...

...sides. 196. The longest side bf any triangle is opposite the greatest angle. 195. In all plane triangles the sum of the three angles is equal to two right angles, or 180 deg. 198. An angle in a segment less than a semicircle is greater than a right angle. 197. An...

...DEH and the angle BAC would together make two right angles. 27 THEOREM. A. ' 72. In every triangle the sum of the three angles 'is equal to two right angles. Pig. 41. Demonstration. Let ABC (fig. 41) be any triangle ; produce the side CA toward D, and draw...

...to the sum of the two angles EFG and EGF, and at the same time equal to EFG alone, which is ahsurd ; therefore the lines AB, CD cannot meet« and must...triangle ABC, the sum of the three angles is equal lo iico right angles. To prove this, you must produce BC (in the Jig. art. Sä,) towards D, then (by...

...equal to the sum of the two angles EFG and EGF, and at the same time equal to EFG alone, whicl: surd ; therefore the lines AB, CD cannot meet, and must be parallel. XXXV. Ill any right lined triangle ABC, the sum of the three angles is equal right angles. To prove this,...

...Cor. 1. Since the angle ACD together with ACB make two right angles, it follows that in every triangle the sum of the three angles is equal to two right angles. Cor. 2. Hence if two angles in one triangle be equal to two in another, the third angle in the one...

...— — , it will become a sin. A = sin. n . cos. c+sin. c . cos. B. But, in every plane triangle, the sum of the three angles is equal to two right angles ; therefore, B and c are equal to the supplement of A : and, consequently, since an angle and its supplement...

...acute angle ; and one which is greater than 90 degrees, is said to |-" obtuse. — In every triangle, the sum of the three angles is equal to two right angles, or 180 degrees. Right angled triangles are in called because the angle included between lhe base and...