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" If two triangles have an angle of one equal to an angle of the other... "
Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Page 172
by Euclid, Rev. John Allen - 1822 - 494 pages
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Practical carpentry, joinery, and cabinet-making [by P. Nicholson. by P ...

Peter Nicholson - Cabinetwork - 1856 - 216 pages
...two lines AD, DB, therefore AB'=AC*+BC9. THEOREM 54,. 125. Two triangles, which have an angle of the one equal to an angle of the other, are to each other as the rectangle of the sides about the equal angles. Suppose the two triangles joined, so as to have...
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Catalogue of the Officers and Students

Trinity College (Hartford, Conn.) - 1870
...have equal bases and equal altitudes are equal. G. Prove that two triangles which have an angle of the one equal to an angle of the other are to each other as the rectangles of the including sides. ENGLISH. I. Correct, criticize, and recast the following...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 368 pages
...similitude of the triangles. PROPOSITION VIII.— THEOREM. 22. Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. Two triangles which have an angle of the one...
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Euclid's Elements of Geometry

Euclid - Geometry - 1872 - 261 pages
...equal angles are reciprocally proportional (AB to BC as LB to BD). And if two triangles (ABD and CBL), have an angle of one equal to an angle of the other, and the sides about the equal angles reciprocally proportional, they will be equal to one another....
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 368 pages
...similitude of the triangles. PROPOSITION VIII.— THEOREM. 22. Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. Two triangles which have an angle of the one...
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Mensuration of lines, surfaces, and volumes

David Munn - 1873
...To find the area of any polygon 43 EXERCISES (4) 44 VIII. Two triangles which have an angle of the one equal to an angle of the other, are to each other as the products of the sides including the equal angles 47 IX. The areas of similar triangles are to...
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The Elementary Geometry of the Right Line and Circle ... With Exercises

William Alexander Willock - Circle - 1875 - 172 pages
...ratio of AO to BO, the sides of the squares, as stated. 27. The Areas of Equiangular Parallelograms are to each other in a Ratio Compounded of the ratios of their Sides. • LetABA,B, and CDC,D, be the equiangular parallelograms, and suppose them so placed...
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Report, Volumes 11-20

1876
...two triangles are similar when they are mutually equiangular. 2. Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. 3. To inscribe A circle in a given triangle....
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 398 pages
...4 ^ QED GEOMETRY. — BOOK IV. PROPOSITION XIII. THEOREM. 341. Two triangles having an angle of the one equal to an angle of the other are to each other as tAe products of the sides including the equal angles. D. Let the triangles ABC and ADE have the...
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Questions and Exercises on Stewart's Lessons in Elementary Physics

George Anthony Hill - Physics - 1880 - 188 pages
...equiangular with respect to each other. (b) K they have their homologous sides proportional. (c) If they have an angle of one equal to an angle of the other, and the sides including these angles proportional. (18) The perpendicular upon the hypothenuse of a...
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