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" The areas of 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'... "
An Elementary Treatise on Plane and Solid Geometry - Page 146
by Benjamin Peirce - 1871 - 150 pages
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Annual Statement, Volumes 11-20

1876 - 646 pages
...polygons. Prove that 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...
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Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...two adjoining sides of the one respectively equal to two adjoining sides of the other, and likewise an angle of the one equal to an angle of the other; the parallelograms are identically equal. [By Superposition.] COR. Two rectangles are equal, if two...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1877 - 458 pages
...the point D toward B, or from it. D2 PROPOSITION XXI. THEOREM. Two triangles are similar when they have an angle of the one equal to an angle of the other, and the sides including those angles proportional. Let the triangles ABC, DEF have the angle A of the one equal to...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 442 pages
...EH AE = B'C'' A'B' B'C' =A'B', Hyp. Ax. 1 Cons. PROPOSITION VI. THEOREM. 284. Two triangles having an angle of the one equal to an angle of the other, and the including sides proportional, are similar. A A' In. the triangles ABC and A' B' С' let /А / Л1 *...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...4 F* = AC1 + SD* + 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 the products cf t he sides including the equal angles. Let the triangles ABC and...
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Exercises on Euclid and in modern geometry, New ed., revised

James McDowell - 1878 - 312 pages
...being taken to form a rectangle, then shall the triangles be equiangular (VI. 5, 16) 54 81. If two triangles have an angle of the one equal to an angle of the other and the rectangle under the sides about the equal angles equal, a side of each triangle being taken to form...
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Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. Phillips - Geometry - 1878 - 236 pages
...ABF " (2, Cor. 3). ABE BE .. . ABC ABD The same is true of parallelograms. BE BF' VI. Theorem. If two triangles have an angle of the one equal to an angle of the other, the ratio of their areas is equal to that of the products of the sides which contain those angles....
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First B.A. Examination, University of London: A Hand-book to the Study of ...

J. G - 1878 - 408 pages
...secant contained between the point and the parallels. 14. // two parallelograms are equal in area, and have an angle of the one equal to an angle of the other, then tfie sides which contain Vie angle of the first are the extremes of a proportion of which the...
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Elementary geometry

James Maurice Wilson - 1878
...have two adjacent sides of the one respectively equal to two adjacent sides of the other, and likewise an angle of the one equal to an angle of the other ; the parallelograms are identically equal. Part. En. Let A BCD, EFGH be two parallelograms which have...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878
...equal (E. 1. 8). I PROP. xix. TIIEOIIEM. (E. 6. 14, 15). Equal triangles and parallelograms laving an angle of the one, equal to an angle of the other, have their sides about th equal angles, reciprocally proportional. And conversely triangles and parallelograms...
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