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" 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, viz. "
Elements of geometry, containing the first two (third and fourth) books of ... - Page 17
by Euclides - 1871
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Plane and Spherical Trigonometry

Alfred Hix Welsh - Plane trigonometry - 1894 - 206 pages
...greater — the half sum. = BCD, since BD = BC; = AEB = CEF. PLANE. Hence, the triangles ADF and CEF have two angles of the one equal to two angles of the other, eacl1 to each, and are therefore similar, since their third angles Л FD and EFC must be equal. But,...
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Euclid's Elements of Geometry, Books 1-6; Book 11

Henry Martyn Taylor - 1895 - 657 pages
...angle of a triangle be at right angles to the base, the triangle is isosceles. PROPOSITION 26. PART 2. If two triangles have two angles of the one equal to two angles of the other, and the sides opposite to a pair of equal angles equal, the triangles are equal in all respects. Let...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 320 pages
...OA2 = OPi :OP2, .'. OP2 is unique. Def. 4th prop., cor. 1 Theorem 8. Triangles are similar if they have two angles of the one equal to two angles of the other, respectively. Given the AA^d, A2B2C2, B, with Z Ai = Z A2, ZG! B^^\X, = ZC2. To prove that AA^Ci —...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 320 pages
...OP1 : OP2 A8 P. .'. OP2 is unique. Def. 4th prop., cor. 1 Theorem 8. Triangles are similar if they have two angles of the one equal to two angles of the other, respectively. Given the AA^d, A2B2C2, with Z A1 = Z A2 , Z G1 = ZC2. To prove that AA^d — A A2B2C2....
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Syllabus of Geometry

George Albert Wentworth - Geometry - 1896 - 50 pages
...triangle is subtracted from two right angles, the remainder is equal to the third angle. 140. Cor. 2. If two triangles have two angles of the one equal to two angles of the other, the third angles are equal. 141. Cor. 3. If two right triangles have an acute angle of the one equal...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 354 pages
...Hence the homologous sides are proportional and the triangles are similar. 261 QED 263. COR. I. If two triangles have two angles of the one equal to two angles of the other, the triangles are similar. 64. COR. II. If two straight lines are cut by a series of parallels, the...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 354 pages
...the homologous sides are proportional and the triangles are similar. 261 Ax. I QED 263. COR. I. If two triangles have two angles of the one equal to two angles of the other, the triangles are similar. ~^~L 264. COR. II. If two straight lines are cut by a series of parallels,...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 354 pages
...sides are proportional and the triangles are similar. 261 QED 263. COR. I. If two triangles hare two angles of the one equal to two angles of the other, the triangles are similar. 264. COR. II. If two straight lines are cut by a series of parallels, the...
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 210 pages
...their sum, the third angle can be found by subtracting this sum from two right angles. 82. COR. 3. If two triangles have two angles of the one equal to two angles of the other, the third angles are equal. 83. COR. 4. A triangle can have but one right angle, or but one obtuse...
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Mathematics: Mechanic's bids and estimates. Mensuration for beginners. Easy ...

Seymour Eaton - 1899 - 340 pages
...EDF. And it has been proved that the angle BAC is not equal to the angle EDF. 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 which is adjacent to the angles that are equal,...
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