...each to 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...

...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...

...In triangles, equal in all 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,...

...PROOF. By 133, from a cut off BD = c. By 100, join AD. Then, because BD = c, :. £ BDA = £ BAD. (126. In an isosceles triangle the angles opposite the equal sides are equal.) And, by 142, the exterior ^ BDA of A CD A > the opposite interior ^ C, :. also £ BAD >£C. Still more...

...£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....

...obtuse-angled triangle the sum of the acute angles is less than a right angle. PROPOSITION XXV. THEOREM. 89. In an isosceles triangle the angles opposite the equal sides are equal. DB Let ABC be an isosceles triangle in which AC and BC are the equal sides. To prove that ZA = Z B....

...the one are respectively equal to a side and the two adjacent angles of the other. PROPOSITION VIII. In an isosceles triangle the angles opposite the equal sides are equal. Corollary. The straight line bisecting the vertical angle of an isosceles triangle bisects the base,...

...same circle be equal ? 4. State four conditions under which triangles are similar. 5. Demonstrate the theorem: — "In an isosceles triangle the angles opposite the equal sides are «qual." 6. Demonstrate the theorem : — " If a line be drawn parallel to the base of a triangle,...