...tangent to a circle, the projection of one straight line upon another, four proportional magnitudes. 2. In an isosceles triangle the angles opposite the equal sides are equal to each other. Every equilateral triangle is also equiangular. An isosceles triangle is symmetric about...

...respectively to a side and two adj. A of the other). QED 111. COROLLARY. Two right triangles are equal when a side and an acute angle of the one are equal 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...

...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...

...to a side and two adj. A of the other). QE D, 111. COROLLARY. Two right triangles are equal when a side and an acute angle of the one are equal respectively...triangle the angles opposite the equal sides are equal. E Let ABC be an Isosceles triangle, having the sides A С and С B equal. We are to prove Z. A = ZB...

...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...

...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...

...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,...

...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...

...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...

...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...