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" If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent. "
Elements of Geometry: With Practical Applications to Mensuration - Page 103
by Benjamin Greenleaf - 1863 - 320 pages
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 714 pages
...(f )2 to a decimal fraction. 10. Extract the square root of 4-20291001. Euclid. 1. If two triangles have two angles of the one equal to two angles of the other, each to each, and the side adjacent to the equal aii'/les in each triangle also equal, then shall the other sides...
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Examination papers used at the examination of candidates for appointment to ...

War office - 1861 - 260 pages
...sovereign and a shilling ? MATHEMATICS. Voluntary Paper, No. II. REV. WN GRIFFIN, MA 1. If two triangles have two angles of the one equal to two angles of the other, and one side equal to one side, namely, the sides which are opposite to equal angles in each, then...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 532 pages
...equal to the right angle EF С (Art. 34, Ax. 9) ; therefore GFE is equal to G С F, or DFE to В С А. Therefore the triangles ABC, DEF have two angles of...each ; hence they are similar (Prop. XXII. Cor.). 206. Scholium. When the two triangles have their sides parallel, the parallel sides are homologous...
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862 - 140 pages
...EDF. Conclusion. — Therefore, if two triangles, &c. QED PROPOSITION 26.— THEOREM. If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side; namely, either the side adjacent to the equal angles in sach, or the...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 pages
...proportional ; and consequently the two triangles are similar (Art. 210). 260. Cor. Two triangles having two angles of the one equal to two angles of the other, each to each, are similar ; since the third angles will also be equal, and the two triangles be equiangular. 261....
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 638 pages
...proportional ; and consequently the two triangles are similar (Art. 210). 260. Cor. Two triangles having two angles of the one equal to two angles of the other, each to each, are similar ; since the third angles will also be equal, and the two triangles be equiangular. 261....
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Elements of Geometry and Trigonometry;: With Practical Applications

Benjamin Greenleaf - Geometry - 1863 - 502 pages
...(Prop. XXVIII. Cor. 5, Bk. I.), and the two angles GFC, GFE are together equal to the right angle EFC (Art. 34, Ax. 9) ; therefore GFE is equal to GCF,...Cor.). homologous. Thus, DE is homologous with AB, DP with AC, and EF with B C. PROPOSITION XXYI. — THEOREM. 267. In any triangle, if a line be drawn...
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Responsions

University of Oxford - Education, Higher - 1863 - 328 pages
...circle, parallelogram, plane superficies. Write out Euclid's three postulates. 2. If two triangles have two angles of the one equal to two angles of the other, each to each, and the sides adjacent to the equal angles also equal, then shall the other sides be equal, each to...
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The Elements of Plane Geometry ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...such that AB is equal to AC, and AD to AE : shew that BE is equal to CD. THEOR. 6. If two triangles have two angles of the one equal to two angles of the other, each to each, and have likewise the sides between the vertices of these angles equal, then the triangles are identically...
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The elements of plane geometry, Volume 1

Mathematical association - 1884 - 146 pages
...that the straight line joining their vertices bisects the vertical angles. THEOR. 19. If two triangles have two angles of the one equal to two angles of the other, each to each, and have likewise the sides opposite to one pair of equal angles equal, then the triangles are identically...
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