 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'...  An Elementary Treatise on Plane and Solid Geometry - Page 146by Benjamin Peirce - 1871 - 150 pagesFull view - About this book
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...trapezoids are then computed by the previous theorems. 198 PROPOSITION VII. THEOREM 414 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. HYPOTHESIS. The & ABC and... | |
 | 1906 - 818 pages
...which touches it. 2. To describe a circle about a given regular pentagon. 3. Equal triangles which have an angle of the one equal to an angle of the other have their sides about those angles reciprocally proportional ; and triangles which have an angle of... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...trapezoids are then computed by the previous theorems. PROPOSITION VII. THEOREM 414 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. HYPOTHESIS. The & ABC and... | |
 | Trinity College (Dublin, Ireland) - 1907 - 536 pages
...points D and E respectively, so that OA : AD = CB : BE, prove that DE is parallel to AB. 8. If two triangles have an angle of the one equal to an angle of the other and the sides about the equal angles reciprocally proportional, prove the triangles equal in area. 9. Given any two... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...is a mean proportional between the segments of the other. 51. Two parallelograms are similar if they have an angle of the one equal to an angle of the other and the including sides proportional. 52. Two rectangles are similar if two adjoining pairs of homologous sides... | |
 | Great Britain. Education Department. Department of Science and Art - 1908 - 328 pages
...and of half its area, from whose sides the given circle shall cut off equal chords. (25) 43. If two triangles have an angle of the one equal to an angle of the other and the sides about those angles proportional, show that the triangles are equiangular to one another. Find a point... | |
 | William Ernst Paterson - Algebra - 1908 - 614 pages
...are equiangular, the ratios of corresponding aides are equal. Theorem III. If two triangles have one angle of the one equal to an angle of the other and the aides about the equal angles proportional, then' the triangles are equiangular. 237. Theorem I leads... | |
 | Michigan. Department of Public Instruction - Education - 1909 - 356 pages
...through a point in the circumference of a circle two chords are drawn, 4. (a) Two triangles having 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) To trisect a right angle.... | |
 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...respectively, to two angles of the other. PROPOSITION XVIII. THEOREM. 368. Two triangles are similar if they have an angle of the one equal to an angle of the other and the including sides proportional. EF Given As ABC and DBF in which XA = XD, and — = — . DE DF To prove... | |
 | George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...Given .-. ZA=ZA'. §282 AABC ABX.AC Then rTT , = , , —— • § 332 (The areas of two triangles that 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.) AABC AB AC 1S, A t'fi'C'... | |
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