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. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'. Plane Geometry - Page 180by Arthur Schultze - 1901Full view - About this book
| J. G - 1878 - 408 pages
...secant contained between the point and the parallels. 14. // two parallelograms are equal in area, and **have an angle of the one equal to an angle of the other,** then tfie sides which contain Vie angle of the first are the extremes of a proportion of which the... | |
| Āryabhaṭa - 1878 - 100 pages
...equal (E. 1. 8). I PROP. xix. TIIEOIIEM. (E. 6. 14, 15). Equal triangles and parallelograms laving **an angle of the one, equal to an angle of the other,** have their sides about th« equal angles, reciprocally proportional. And conversely triangles and parallelograms... | |
| James Maurice Wilson - 1878 - 450 pages
...have two adjacent sides of the one respectively equal to two adjacent sides of the other, and likewise **an angle of the one equal to an angle of the other** ; the parallelograms are identically equal. Part. En. Let A BCD, EFGH be two parallelograms which have... | |
| George Albert Wentworth - 1879 - 196 pages
...PAGE 217. Ex. i. Show that two triangles which have an angle of the one equal to the supplement of the **angle of the other are to each other as the products of the sides including the** supplementary angles. Let A ABC and CDE have AACB and DCE supplements of each other. Place these A... | |
| William Frothingham Bradbury - Geometry - 1880 - 260 pages
...we have AB:AG — AC:AH But by hypothesis AB : D F.= AC : DF THEOREM XXIV. 60i Two triangles having **an angle of the one equal to an angle of the other,** and the sides including these angles proportional, are similar. In the triangles ABC, DBF let the angle... | |
| District of Columbia. Board of Education - Education - 1881 - 314 pages
...TENTH GRADE. MAY itf. GEOMETRY AND TRIGONOMETRY. (Twenty credits.) 1. Theorem: — Two triangles having **an angle of the one equal to an angle of the other,** and the sides including these angles proportional, are similar. 2. If from the diagonal BD of a square... | |
| George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...Wo'' A'B' ~ We'Hyp. Ax. 1 Since AE = A' B', Cons. PROPOSITION VI. THEOREM. 284. Two triangles having **an angle of the one equal to an angle of the other,** and the including sides proportional, are similar. A A' In the triangles ABC and A' B' C' let -. A'B'... | |
| George Albert Wentworth - Geometry, Modern - 1882 - 268 pages
...squares on the diagonals. GEOMETRY. — BOOK IV. PROPOSITION XIII. THEOREM. 341. Two triangles having **an angle of the one equal to an angle of the other...products of the sides including the equal angles.** Let the triangles ABC and AD E have the common angle A. TT . АABС We are to prove AB X AC Draw B... | |
| Great Britain. Education Department. Department of Science and Art - 1882 - 510 pages
...the same subject. The values attached to the questions differ little from one another. 1. Prove that **two triangles, which have an angle of the one equal to an angle of the other,** and the sides including the equal angles proportional, are similar. A diagonal of a parallelogram is... | |
| George Albert Wentworth - Geometry, Modern - 1879 - 262 pages
...the squares on the diagonals. PEOPOSITION XIII. THEOREM. 341. Two triangles having an angle of ihe **one equal to an angle of the other are to each other as the products** of 1 fie sides including the egtial angles. Let the triangles ABC and AD E have the common angle A.... | |
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