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" Two triangles which have an angle of one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles. "
Plane and Solid Geometry - Page 164
by Claude Irwin Palmer, Daniel Pomeroy Taylor - 1918 - 436 pages
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - Astronomy - 1822 - 516 pages
...HG, and of PB to BL or HE. Cor. 1. — By a similar reasoning it may be proved, that triangles, which have an angle of one, equal to an angle of the other, are to each other, in a ratio, compounded of the ratios, of the sides including the equal angles. Cor. 2. — A right...
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The New Practical Builder and Workman's Companion, Containing a Full Display ...

Peter Nicholson - Architecture - 1823 - 210 pages
...the two lines AD, DB, therefore AB2 = AC2 THEOREM 63. 161. 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 Suppose* the two triangles joined, so as to have a common angle,...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 166 pages
...have their sides about the equal angles reciprocally proportional : and triangles are equal, which have an angle of one equal to an angle of the other, and the sides about the equal angles reciprocally proportional. Given two equal triangles ABC, ADE,...
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846 - 272 pages
...equal angles are reciprocally proportional (AB to BC as 1.I! 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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Elements of Geometry, Theoretical and Practical: Containing a Full ...

George Clinton Whitlock - Mathematics - 1848 - 340 pages
...(147) with (148).] Of PROPOSITION III. Two triangles, having an angle of the one equal to an (159) angle of the other, are to each other as the products of the sides about the equal angles. Let the equal apgles of the triangles A, B, be made vertical, and join the...
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Elements of geometry and mensuration

Thomas Lund - Geometry - 1854 - 520 pages
...be : BC ; and by making C the centre, that be : BC :: ac : AC. COR. 1. Conversely, if two triangles have an angle of one equal to an angle of the other, and the sides forming the equal angles proportionals, the triangles will be similar. COR. 2. Hence,...
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Practical carpentry, joinery, and cabinet-making [by P. Nicholson. by P ...

Peter Nicholson - Cabinetwork - 1856 - 518 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 a common...
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Modern Methods in Elementary Geometry

E. M. Reynolds - Geometry - 1868 - 172 pages
...A'B'C'. Relation of Areas of Figures. THEOREM VI. Triangles which have one angle of the one equal to one angle of the other, are to each other as the products of the sides containing the equal angle. Let the triangles ABC, A'BC' have equal angles at B. Then shall ABC : A'BC'...
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Catalogue of the Officers and Students

Trinity College (Hartford, Conn.) - 1870 - 1008 pages
...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 sentences:...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...GEOMETRY.— BOOK IV. THEOREMS. 219. Two triangles which have an angle of the one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles. (IV. 22.) 220. Prove, geometrically, that the square described upon the sum of...
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