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" If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects. "
Elementary Geometry: With Applications in Mensuration - Page 10
by Charles Davies - 1850 - 216 pages
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 532 pages
...construction, AG is equal to DE ; hence А П is equal to D F. Therefore the two triangles AGH, DEF, having two ¡sides and the included angle of the one equal to...and the included angle of the other, each to each, are themselves equal (Prop. V. Bk. I.). But the triangle AGH is similar to А В С ; therefore DEF...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 pages
...sides of the same square ; and BF equal to BC, for the same reason ; therefore the triangles ABF, HBC have two sides and the included angle of the one equal to two sides and the included angle of the other ; hence they are themselves equal (Prop. V. Bk. I.). G ELEMENTS OF GEOMETRY. EG same altitude...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 638 pages
...sides of the same square ; and BF equal to BC, for the same reason ; therefore the triangles ABF, HBC have two sides and the included angle of the one equal to two sides and the included angle of the other; hence they arc themselves equal (Prop. V. Bk. I.). EG ELEMENTS OF GEOMETRY. same altitude...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...sides of the same square ; and BF equal to BC, for the same reason ; therefore the triangles ABF, HBC have two sides and the included angle of the one equal to two sides and the included angle of the other ; hence they are themselves equal (Prop. V. Bk. I.). ELEMENTS OF GEOMETRY. K same altitude...
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Primary Elements of Plane and Solid Geometry: For Schools and Academies

Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...similar. • Take AG equal to DE, and AH to DF ; also, join GH. Then the triangles AGH, DEF, having two sides and the included angle of the one equal to two sides and the included angle of the other, are equal throughout (Theo. VII, B. I). Now,- by hypothesis, AB : DE : : AC : DF. Therefore,...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - 1863 - 436 pages
...is equal to the angle CEB\ THEOREM IVIf two triangles have two sides and the included angle of tie one, equal to two sides and the included angle of the other, each to each, the two triangles will be equalLet the triangles ABC and DEF have the side AC equal to DF, CB to FE,...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...be greater nor less than D : hence, it must be equal to it. The two triangles have, therefore, two sides and the included angle of the one equal to two sides and the inclu* ded angle of the other, each to each ; and, consequently, they are equal in all their parts...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1864 - 358 pages
...Dl equal to AC and DG equal to AB, and join IG- Then the two triangles ABC and DIG, having two s1des and the included angle of the one equal to two sides and the included ingle of the other, each to each, will be equal (Bk- I Th- iv) Hence, the angles / and G are equal...
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Elements of plane geometry, book i, containing nearly the same propositions ...

Euclides - 1865 - 80 pages
...and C to DFE, the equal angles being always opposite to the equal sides. PROPOSITION XII. TIIEOR. If two triangles have two sides, and the included angle...and the included angle of' the other, each to each, the triangles are equal (Def. 37). Let the two triangles ABC and EDF have the side AB equal to DE,...
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Outlines of Mathematical Science for the School Room

Charles Davies - Mathematics - 1867 - 186 pages
...three sides of the other, each to each, the triangles will be equal in all their parts." Prop. V. " If two triangles have two sides and the included angle...and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing,...
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