 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...equal, respectively, to two angles of the other, the triangles are similar. § 250. (3) If two triangles have an angle of one equal to an angle of the other, and the sides including these angles proportional, the triangles are similar. § 251. (4) If the ratios... | |
 | Education - 1902 - 942 pages
...diagonal of the smaller pentagon. 5. 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. 12, ABCD is a trapezium in which AB is parallel to and greater than DC, BD meets AC in E, and DF is... | |
 | 1902 - 482 pages
...same altitude are to one another as their bases. 5. Equal parallelograms which nave an angle of the one equal to an angle of the other, have their sides about those angles reciprocally proportional. 6. Describe a rectilineal figure which shall be similar to... | |
 | John Alton Avery - Geometry, Modern - 1903 - 136 pages
...triangle, a smaller triangle is formed similar to the given triangle. THEOREM V 164. If two triangles have an angle of one equal to an angle of the other, and the including sides proportional, the triangles are similar. Hyp. In the A RST and R'S'T', let... | |
 | James McMahon - Geometry, Plane - 1903 - 382 pages
...Similarly, it may be proved that B"C" = B'C'. Two sides and included angle. 44. THEOREM 10. If two triangles have an angle of one equal to an angle of the other, and the sides about these angles proportional, then the triangles are similar. Let the triangles ABC... | |
 | American School (Chicago, Ill.) - Engineering - 1903 - 390 pages
...A', and ^^_ = — — A. 1 1 ./Y li Therefore the triangles ABE and A' B' E' are similar, for they have an angle of one equal to an angle of the other, and the sides including these angles proportional (Theorem LIII). Again, since the polygons are similar,... | |
 | University of Sydney - 1904 - 680 pages
...respectively measure 1 ft. and " ft. 1 in. 7. 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. 8. Find the weight of a conical piece of metal, whose height is 3 ft., and the radius of its base 2... | |
 | Euclid - Euclid's Elements - 1904 - 488 pages
...14. THEOREM. Parallelograms which are equal in area, and which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. Conversely, parallelograms which have one angle of the one equal to one angle of the other, and the... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...is similar to A ABC). Art. 306. Art. 101. Ax. 8. QED PROPOSITION XVII. THEOREM 327. If two triangles have an angle of one equal to an angle of the other, and the including sides proportional, the triangles are similar. Given the A ABC and A'B'C', in which... | |
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Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional ; and parallelograms that have one angle of the one equal to one angle of the other, and their sides... 
