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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... "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Page 94
by Dennis M'Curdy - 1846 - 138 pages
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 460 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...
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Report of the Committee of Council on Education in Scotland...[without Appendix]

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...
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Annual Report of the Commissioners ..., Volume 68

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...
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Interim Report of the Commissioners on Certain Parts of Primary Education ...

New South Wales. Commission on primary, secondary, technical, and other branches of education - Education - 1903 - 634 pages
...and a diagonal of the smaller pentagon. 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. A BCD is a trapezium in which Л В is parallel to and greater than DC, BD meets AC in E, and DF is...
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Plane Geometry by the Suggestive Method

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...
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Elementary Geometry: Plane

James McMahon - Geometry, Plane - 1903 - 380 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...
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Mathematics, mechanics, heat

American School (Chicago, Ill.) - Engineering - 1903 - 392 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,...
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Calendar of the University of Sydney

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...
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A Text-book of Euclid's Elements for the Use of Schools, Book 1

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...
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Plane Geometry

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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