 | 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... | |
 | Canada. Department of the Interior - 1888 - 756 pages
...figures. 13. Triangles and parallelograms having equal bases are to one another as their altitudes. 14. If two triangles have one angle of the one equal to one angle of tho other, the triangles are to each other in the ratio of the rectangles under the sides containing... | |
 | 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 - 1004 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 - 356 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... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...the rectangle contained by the sides about the other, the triangles are equal. (ii.) Conversely: — If two triangles have one angle of the one equal to one angle of the other, the rectangle contained by the sides about one of those angles is equal to the rectangle contained... | |
 | 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... | |
 | Queensland. Department of Public Instruction - Education - 1890 - 526 pages
...segments of the base. What is the corresponding proposition for the external bisector ? 8. Triangles which have one angle of the one equal to one angle of the other, have to one another the ratio which is compounded of the ratios of the sides about the equal angles.... | |
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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. 
