| Edinburgh Mathematical Society - Mathematics - 1899
...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.... | |
| University of Toronto - 1900
...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... | |
| Great Britain. Board of Education - Boys - 1900 - 531 pages
...smaller circle. 7. Define the terms submultiple, ratio, homologous, duplicate ratio. 8. If two triangles **have one angle of the one equal to one angle of the other, and** the sides about the equal angles proportionals, the triangles shall be similar. In a given straight... | |
| Euclid, Micaiah John Muller Hill - Euclid's Elements - 1900 - 143 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... | |
| M. J. M. HILL - 1900
...PROPOSITION XLVIII. (i). (Euc. VI. 14, 1st Part.) ENUNCIATION. Parallelograms having equal areas and having **one angle of the one equal to one angle of the other** have the sides about the equal angles reciprocally proportional. Let the two parallelograms be placed... | |
| Thomas Franklin Holgate - Geometry - 1901 - 440 pages
...right angle which make equal angles with one of the sides. MISCELLANEOUS EXERCISES 1. If two triangles **have one angle of the one equal to one angle of the other, and** a second angle of the one supplementary to a second angle of the other, then the sides about the third... | |
| Macmillan & Co - Textbooks - 1901 - 776 pages
...addition, . a + b+e+ ... x+y+z+ ... or a:x 338 EUCLID'S ELEMENTS. PROPOSITION 6. THEOREM. If two triangles **have one angle of the one equal to one angle of the other, and** the sides about the equal angles proportionals, the triangles shall be similar. In the A' BAG, EOF,... | |
| Education - 1902
...pentagon is equal to the sum of a side and a 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... | |
| Charles Godfrey, Arthur Warry Siddons - Geometry - 1903 - 355 pages
...join PQ ; measure L.' P, Q, and compare them with L.' B, C. =o fig. 313. THEOREM 5. 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. fig. 314. Data ABC, DEF... | |
| Education - 1903
...triangles are equiangular their corresponding sides are proportional ; and the converse. 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. The internal bisector of... | |
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