...is equilateral and its sides are quadrants. PROPOSITION XV. Theorem. — In an isosceles spherical triangle the angles opposite the equal sides are equal ; and, conversely, If two angles of a spherical triangle are equal, the triangle is isosceles. DEM.— Let ABC be an isosceles spherical...

...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...

...the greater is twice the less; find what fraction the less is of four right angles. ' ^~ THEOREM VI. In an isosceles triangle, the angles opposite the equal sides are equal. Let ABC be an isosceles triangle, having the side AB equal to the side AC; then will the angle B, opposite...

...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...

...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...

...4NAC = 4ACB, (168. If a transversal cuts two parallels, the alternate angles are equal.) 4 ACS = (126. In an isosceles triangle the angles opposite the equal sides are equal.) £ ABC = £ DAN, (169. If a transversal cuts two parallels, the corresponding angles are equal.) **...

...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,...

...£ACB, (168. If a transversal cuts two parallels, the alternate angles are equal.) 4 ACB = 4 ABC, (126. In an isosceles triangle the angles opposite the equal sides are equal.) 4 ABC = 4 DAN, (169. If a transversal cuts two parallels, the corresponding angles are equal.) (128....