 | 1897 - 154 pages
...the same arc. Deduce that all angles in the same segment of a circle are equal to one another. 4. If two triangles have one angle of the one equal to one angle of tt;e oiher, and the sides about the equal angles proportionals, shew that the triangles are similar.... | |
 | 1899 - 802 pages
...Shew that the area of the hexagon is threefourths that of the regular circumscribed hexagon. 3. If two triangles have one angle of the one equal to one...about the equal angles proportionals, the triangles are similar. If the perpendicular from the vertex of a triangle to the base falls within the triangle... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 412 pages
...§ 86, cor. 5, they can be proved to be mutually equiangular. PROPOSITION XVIII. ^. 264. Theorem. If two triangles have one angle of the one equal to one angle of the other, and the including sides proportional, the triangles are similar. A, B, Given A AlBlCl, A2B2C2, such that Z... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...parallel or perpendicular to the sides of the other, they are similar. PROPOSITION XVIII. 264. Theorem. If two triangles have one angle of the one equal to one angle of the other, and the including sides proportional, the triangles are similar. C, Given A A1B^i, AJB^C2, such that Z Ci =... | |
 | Edinburgh Mathematical Society - Electronic journals - 1899 - 340 pages
...joined, the triangles EAB, DAC are halves of the parallelograms BE, CD. Hence, Two triangles which have one angle of the one equal to one angle of the other have to each other the same ratio as the rectangles contained by the sides about the equal angles.... | |
 | Great Britain. Board of Education - Boys - 1900 - 566 pages
...inscribed in the smaller circle. 7. Define the terms submultiple, ratio, homologous, duplicate ratio. 8. If two triangles have one angle of the one equal to one...equal angles proportionals, the triangles shall be similar. In a given straight Hue PQ a point M is taken and PQ is produced to Ü so that MO is a mean... | |
 | Great Britain. Parliament. House of Commons - Great Britain - 1900 - 686 pages
...submultiple, ratio, homologous, duplicate ratio. 8. If two triangles have one angle of the one equal to on« angle of the other, and the sides about the equal angles proportionals, the triangles shall lx) similar. In a given straight line PQ a point M is taken and PQ is produced to 0 so that MO is a... | |
 | University of Toronto - 1900 - 1164 pages
...the other, have their sides about the equal angles reciprocally proportional ; and triangles which have one angle of the one equal to one angle of the other and their sides about the equal angles reciprocally proportional are equal to one another. Use this proportion... | |
 | Euclid, Micaiah John Muller Hill - Euclid's Elements - 1900 - 190 pages
...about the equal angles reciprocally proportional, are equal in area. 49. (i) Equal triangles which have one angle of the one equal to one angle of the other have their sides about the equal angles reciprocally proportional. (ii) Triangles which have one angle... | |
| |
If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar. 
