| 1884 - 610 pages
...a given circle. Inscribe a regular figure of ten sides in a given circle. 3. 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. If one of the said sides in the... | |
| Euclides - 1884 - 434 pages
...= ir BC: ir FE; • ||m AB : ||m FE = ir BC: r FE; PROPOSITION 15. THEOREMS. 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. Conversely : Triangles which have... | |
| George Bruce Halsted - Geometry - 1885 - 389 pages
...equal.) therefore, by 491, GH = BH'. In the same way HF = H'F', THEOREM VII. 511. Two triangles having **one angle of the one equal to one angle of the other, and** the sides about these angles proportional, are similar. HYPOTHESIS. £ B = £ G, and AB : BC : : FG... | |
| George Bruce Halsted - Geometry - 1886 - 394 pages
...equal.) therefore, by 491, GH = BH'. In the same way HF = H'F', THEOREM VII. 511. Two triangles having **one angle of the one equal to one angle of the other, and** the sides about these angles proportional, are similar. HYPOTHESIS. £ B = $. G, and AB : BC : : FG... | |
| Association for the Improvement of Geometrical Teaching - Euclid's Elements - 1888 - 208 pages
...GH. Therefore AB : CD : : EF : GH. IV. 14, Part ii. QED THEOR. 14. If two triangles or parallelograms **have one angle of the one equal to one angle of the other,** their areas have to one another the ratio compounded of the ratios of the including sides of the first... | |
| New Brunswick. Board of Education - Education - 1889 - 1006 pages
...and those which are opposite to the equal angles are homologous sides. 6. 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. N. В.- --Female candidates will... | |
| E. J. Brooksmith - Mathematics - 1889 - 354 pages
...are the middle points ofAB, CD, prove that PQ_ is parallel to AC and BD. 10. 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 ; and, conversely, triangles which... | |
| Royal Military College, Sandhurst - Mathematics - 1890 - 144 pages
...the line joining two alternate vertices of a given length. 7. Prove that 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. 8. In a right-angled triangle, show... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...parallelograms as in VI. 23, ||gm AC : ||gm CF :: rect. BC, CD : rect. EC, CG. Ex. 717. — Triangles which **have one angle of the one equal to one angle of the other** are to one another in the ratio compounded of the ratios of the sides containing the equal angles.... | |
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