 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
 | Encyclopedias and dictionaries - 1920 - 934 pages
...its sides. Triangles which have their homologous sides proportional are similar. Two triangles which have an angle of the one equal to an angle of the other, and the sides about these angles proportional, are similar. Two triangles which have their sides parallel or perpendicular,... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...to the sum of three given squares. PROPOSITION XIII. THEOREM 378. 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. Given A ABC and A'B'C',... | |
 | Encyclopedias and dictionaries - 1920 - 934 pages
...its sides. Triangles which have their homologous sides proportional are similar. Two triangles which have an angle of the one equal to an angle of the other, and the sides about these angles proportional, are similar. Two triangles which have their sides parallel or perpendicular,... | |
 | Edinburgh Mathematical Society - Electronic journals - 1920 - 460 pages
...collinear. The theorem in similarity corresponding to the converse theorem (2) is the following : If two triangles have an angle of the one equal to an angle of the other and another pair of angles supplementary, then the sides opposite to the equal angles are proportional... | |
 | Robert Remington Goff - 1922 - 136 pages
...330. Two triangles with equal altitudes are to each other as their bases. *331. 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. *332. Two similar triangles... | |
 | Edson Homer Taylor, Fiske Allen - Mathematics - 1923 - 104 pages
...right triangles having an acute angle of the one equal to an acute angle of the other. 3. They have one angle of the one equal to an angle of the other and the including sides proportional. 4. The three sides of one are proportional to the three sides of the... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...left to the student.] PLANE GEOMETRY PROPOSITION XIII. THEOREM 378. 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. Given A ABC an4 A'B'C',... | |
 | Baltimore (Md.). Department of Education - Mathematics - 1924 - 182 pages
...similar, if: 1. They have two angles of one respectively equal to two angles of the other. 2. They have an angle of the one equal to an angle of the other and the including sides proportional. 3. The sides of one are respectively proportional to the sides of the... | |
 | William Weller Strader, Lawrence D. Rhoads - Geometry, Plane - 1927 - 434 pages
...parallel; (3) have their respective sides perpendicular; (4) have their respective sides proportional; (5) have an angle of the one equal to an angle of the other and the including sides proportional; (6) are similar to the same triangle; Polygons are similar, if they (1)... | |
 | University of Adelaide. Public Examinations Board - Examinations - 1928 - 1280 pages
...corresponding sides of two triangles are proportional, the triangles are equiangular. Triangles which have an angle of the one equal to an angle of the uther, and the sides about the equal angles proportional, are similar. The bisectors of an angle of... | |
| |
