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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. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'. "
Plane Geometry - Page 180
by Arthur Schultze - 1901
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College Entrance Examination Papers in Plane Geometry

Geometry, Plane - 1911 - 192 pages
...parts of equal area? (6) Trisect a right angle, and explain your construction. 6. If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, prove that the two triangles are similar. 6. The angle of a sector...
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Bulletin, Issues 1-13

United States. Office of Education - 1911 - 1154 pages
...line. Group II. 4. Prove that two tetrahedrons having a trihedral angle of one equal to a trihedral angle of the other, are to each other as the products of the edges including the equal trihedral angles. 5. Prove that the volume of a triangular pyramid is equal...
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Key to Elementary Geometry, Plane

John Charles Stone - 1911 - 110 pages
...This is the side of the square. Ex. 3. When an isosceles triangle is constructed, the two areas are to each other as the products of the sides including the equal angles ( 277). Imagine the construction made. Since the areas are equal, CAXCB = CDXCE = CD\ or ~=^. CA...
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Elementary Trigonometry

William Ernst Paterson - Logarithms - 1911 - 262 pages
...each, and a side of the one equal to the corresponding side of the other. Prop. 9. If two triangles have an angle of the one equal to an angle of the other, and the sides about another pair of angles equal, each to each, then the third angles are either equal...
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Solid Geometry

Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - Geometry, Solid - 1912 - 222 pages
...perimeter multiplied by the radius of the inscribed circle. 498. Two triangles which have an angle of one equal to an angle of the other are to each other...products of the sides including the equal angles. 503. Two similar triangles are to each other as the squares of any two homologous sides. 517. If the...
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Solid Geometry

Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - Geometry, Solid - 1912 - 216 pages
...PROPOSITION XIV. THEOREM 810. Two triangular pyramids, having a trihedral angle of one equal to a trihedral angle of the other, are to each other as the products of the edges including the equal trihedral angles. Given triangular pyramids 0-ACD and Q-FGM with trihedral...
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Plane Geometry

William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...THEOREM 337. If two triangles have an angle of one equal to an angle of the other, their areas are to each other as the products of the sides including the equal angles. Given two triangles ABC and A'B'C', having the angle A equal to the angle A'. To prove that AABC bc...
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Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...THEOREM 337. If two triangles have an angle of one equal to an angle of the other, their areas are to each other as the products of the sides including the equal angles. c' zc Given two triangles ABC and A'B'C', having the angle A equal to the angle A'. To prove that AABC...
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Plane and Solid Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...PROPOSITION XIV. THEOREM 810. Two triangular pyramids, having a trihedral angle of one equal to a trihedral angle of the other, are to each other as the products of the edges including the equal trihedral angles. Given triangular pyramids O-ACD and Q-FGM with trihedral...
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Elements of Solid Geometry

William Herschel Bruce, Claude Carr Cody - Geometry, Solid - 1912 - 134 pages
...edges. PROPOSITION XX. THEOREM 665. Tetrahedrons having a trihedral angle of one equal to a trihedral angle of the other are to each other as the products of the edges about the equal trihedral angles. T "-<. \ ^^* AD Given two tetrahedrons T-ABC and T'-DEF, with...
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