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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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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...we have AB:AG — AC:AH But by hypothesis AB : D F.= AC : DF THEOREM XXIV. 60i Two triangles having an angle of the one equal to an angle of the other, and the sides including these angles proportional, are similar. In the triangles ABC, DBF let the angle A = D and...
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Report of the Board of Education to the Commissioners of the District of ...

District of Columbia. Board of Education - Education - 1881 - 314 pages
...TENTH GRADE. MAY itf. GEOMETRY AND TRIGONOMETRY. (Twenty credits.) 1. Theorem: — Two triangles having an angle of the one equal to an angle of the other, and the sides including these angles proportional, are similar. 2. If from the diagonal BD of a square ABCD, BE be...
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Elements of Geometry

George Albert Wentworth - 1881 - 266 pages
...squares on the diagonals. GEOMETRY. — BOOK IV. PROPOSITION XIII. THEOREM. 3-41. Two triangles having an angle of the one equal to an angle of the other are to each other an the products of the sides including the equal angles. Let the triangles ABC and...
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Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1882 - 512 pages
...the ratio of AN to NB is the duplicate of the ratio of AM to MB. 2. If two triangles of equal area have an angle of the one equal to an angle of the other, prove that the sides about the equal angles are reciprocally proportional. 3. Shew how to divide a...
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883
...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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The Eclectic School Geometry

Evan Wilhelm Evans - Geometry - 1884 - 149 pages
...; hence, it is also similar to DFE. Therefore, two triangles, etc. THEOREM XI. Two triangles having an angle of the one equal to an angle of the other, and the sides about those angles proportional, are similar. Let the two triangles ABC, DEF, have the angle A equal...
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The Eclectic School Geometry: A Revision of Evan's School Geometry

Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...AO parallel to BC. M ANC = ACN = CAO. ANC = CBA + BAN. Complete the proof. 24. 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 in- B eluding the equal angles. See Theo. VII. BAC :...
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The elements of plane geometry, Volume 1

Mathematical association - 1884
...two adjoining: sides of the one respectively equal to two adjoining sides of the other, and likewise an ang:le of the one equal to an angle of the other ; the parallelograms are identically equal. Let ABCD, EFGH be two parallelograms having the angle ABC...
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The Elements of Plane Geometry ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 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. Let ABCD, EFGH be two parallelograms having the angle ABC...
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The Common Sense of the Exact Sciences

William Kingdon Clifford - Mathematics - 1885 - 314 pages
...famous proposition about parallel lines.1 The first of these deductions will now show us that if two triangles have an angle of the one equal to an angle of the other and the sides containing these angles respectively equal, they must be equal in all particulars. For if we take up...
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