The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw... Elements of Geometry - Page 63by Adrien Marie Legendre - 1825 - 224 pagesFull view - About this book
| Dennis M'Curdy - Geometry - 1846 - 166 pages
...about the equal angles reciprocally proportional : and triangles are equal, which have an angle of one equal to an angle of the other, and the sides about the equal angles reciprocally proportional. Given two equal triangles ABC, ADE, having equal angles at A. Place the... | |
| Euclides - 1846 - 272 pages
...right, since they are equal to these right angles (by Prop. 34.) CoR. 2. — If two parallelograms have an angle of the one equal to an angle of the other, the remaining angles will be also equal ; for the angles which are opposite to these equal angles are... | |
| George Roberts Perkins - Geometry - 1847 - 326 pages
...Therefore, by equality of ratios, we have AC : GK : : CD : KL. Hence the two triangles ACD and GKL have an angle of the one equal to an angle of the other, and the sides about those angles proportional, and consequently the triangles are similar. In the same manner it might... | |
| George Clinton Whitlock - Mathematics - 1848 - 338 pages
...Trapezoid— -consequences, measures, parallelogram, triangle, comparisons, equalities 92 3. Triangles having an angle of the one equal to an angle of the other — consequence • 93 4. Exercises.... 94 BOOK THIRD. PLANE GEOMETRY DEPENDING ON THE CIRCLE, ELLIPSE,... | |
| George Clinton Whitlock - Mathematics - 1848 - 340 pages
...Trapezoid — consequences, measures, parallelogram, triangle, comparisons, equalities 92 3. Triangles having an angle of the one equal to an angle of the otherconsequence 93 4. Exercises 94 BOOK THIRD. PLANE GEOMETRY DEPENDING ON THE CIRCLE, ELLIPSE, HYPERBOLA,... | |
| Elias Loomis - Conic sections - 1849 - 252 pages
...similar. Wherefore, two triangles, &c. PROPOSITION XX. THEOREM. Two triangles are similar, when they have an angle of the one equal to an angle of the other, and the sides containing those angles proportional. Let the triangles ABC, DEF have the angle A of the one, equal... | |
| Charles Davies - Trigonometry - 1849 - 372 pages
...triangles include, by implication, those of all figures. PROPOSITION XX. THEOREM. Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar. In the two triangles ABC, DEF, let the angles A... | |
| George Roberts Perkins - Geometry - 1850 - 332 pages
...Therefore by equality of ratios, we have AC : GK : : CD : KL. Hence the two triangles ACD and GKL have an angle of the one equal to an angle of the other, and the sides about those angles proportional, and consequently the triangles are similar. In the same manner it might... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...implication, those of all figures. B 109 D DF., PROPOSITION XX. THEOEEM. Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar. Let ABC, DEF, be two triangles, having the angle... | |
| Euclid - Geometry - 1853 - 176 pages
...Hypoth. (41 I.29. (c) I. 26. fa) I. 29. (6) Hypoth. (c) I. 34. COROLLARY 2. If two parallelograms have an angle of the one equal to an angle of the other, the remaining angles shall be respectively equal. For the angles opposite the equal angles are equal... | |
| |