...line. 90. Def. Segments of a straight line are the parts into which it is divided. • THEOREM IX. 91. In an isosceles triangle the angles opposite the equal sides are equal to cach other. Hypothesis. ABC a triangle in which CA = CB. Conclusion. Angle A = angle B. Proof. Bisect...

...respectively to an homologous side and acute angle of the other. TRIAXGLKS. PROPOSITION XXVIII. THEOREM. 112. In an isosceles triangle the angles opposite the equal sides are equal. С Let ABC be ал isosceles triangle, having the sides AC and С B equal. We are to prove ¿ A = ¿...

...and an acute angle of the other. ВЕЪАТКШ BETWEEN THE PARTS OF A TRIANGLE. THEOREM XXXI. 94. In an isosceles triangle, the angles opposite the equal sides are equal. In the isosceles A ABC, let AC and B С be the equal sides. С ADB To prove that ¿- a = ¿- b. Let...

...equal in all their parts (Th. IV)', and, consequently, the angle B is equal to the angle C. Therefore, in an isosceles triangle, the angles opposite the equal sides are equal. Cor. I.—An equilateral triangle is equiangular. For, if AB equals AC, then, by the Theorem just proved,...

...chords are equal, the arcs are, and hence the angles subtended by these arcs. 223. COROLLARY 3. — In an isosceles triangle the angles opposite the equal sides are equal ; and, conversely, if two angles of a triangle are equal, the sides opposite are equal, and the triangle...

...any exterior angle is greater than either of the opposite interior, QED 35. We shall next show that, In an isosceles triangle, the angles opposite the equal sides are equal. In the triangle ABC, let AB = AC (Fig. 2), Turn the triangle ABC over, and suppose it to take the position...

...each. 39. Corollary. Two right triangles are equal if their legs are equal, each to each. 40. Theorem. In an isosceles triangle the angles opposite the equal sides are equal. 41. Corollary. An equilateral triangle is equiangular. 42. Theorem. If in a triangle two angles are...

...contained by the whole and one of the parts may be equal to the square on the other part. (LEGENDRE.) 1. In an isosceles triangle the angles opposite the equal sides are equal. 2. In equal circles, equal chords are equally distant from the centres ; and of two unequal chords...

...any exterior angle is greater than either of the opposite interior, QED 35. We shall next show that, In an isosceles triangle, the angles opposite the equal sides are equal. In the triangle ABC, let AB = AC {Fig. 2), Fig.2 "Turn the triangle ABC over, and suppose it to take...

...respects, the equal sides lie opposite the equal angles ; and conversely. PROPOSITION XI. THEOREM. In an isosceles triangle the angles opposite the equal sides are equal. BOOK I. Join the vertex A and the middle point D of the base BC. Then, AB is equal to AC, by hypothesis,...