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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. "
Elements of Plane Geometry - Page 48
by Thomas Hunter - 1878 - 132 pages
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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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Elements of Geometry and Trigonometry

C. Davies - 1867 - 342 pages
...DEB (Ax- 3)In the same manner we may prove that the angle AED ia equal to the angle CEBTHEOREM IV- If two triangles have two sides and the included angle of the one, equal to two sides and ike included angle of the other, each to each, the two triangles will be equalLet the triangles ABC...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1868 - 338 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. Y. Bk. I.). G same altitude BD (Prop. II. Cor....
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Marks' First Lessons in Geometry: Objectively Presented

Bernhard Marks - Geometry - 1869 - 172 pages
...What do you think of the areas of the triangles ? d bcef DEMONSTRATION. We wish to prove, that, If two triangles have two sides, and the included angle...and the included angle of the other, each to each, the two triangles are equal in all respects. Let the triangles abc and d ef have the side ab of the...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1869 - 472 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...the included angle of the other, each to each ; and, consequently, they are equal in all their parts (PV) ; which was to be proved. Scholium. In triangles,...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1869 - 516 pages
...construction, AG is equal to DE ; hence AH is equal to D F. Therefore the two triangles AGH, DEF, having two sides and the included angle of the one equal to two...and the included angle of the other, each to each, are themselves equal (Prop. V. Bk. I.). But the triangle AGH is similar to ABC ; therefore DEF is also...
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Marks' First Lessons in Geometry: In Two Parts : Objectively Presented and ...

Bernhard Marks - Geometry - 1871 - 172 pages
...What do you think of the areas of the triangles ? a •/ DEMONSTRATION. We wish to prove, that, If two triangles have two sides, and the included angle...and the included angle of the other, each to each, the two triangles are equal in all respects. Let the triangles ale and def have the side ab of the...
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An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Plane - 1870 - 304 pages
...greater is greater than the angle opposite the less (76). On the equality of triangles. 12. When two triangles have two sides and the included angle of the one respectively equal to two sides and the included angle of the other, the triangles are equal in all...
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Marks' First Lessons in Geometry: In Two Parts : Objectively Presented and ...

Bernard Marks - Geometry - 1871 - 172 pages
...What do you think of the areas of the triangles ? d bcef DEMONSTRATION. We wish to prove, that, If two triangles have two sides, and the included angle...and the included angle of the other, each to each, the two triangles are equal in all respects. Let the triangles abc and d ef have the side ab of the...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 pages
...because AB is equal to CD, and BC is common to the two triangles <VBC BCD, the two triangles ABC, BCD have two sides and the included angle of the one, equal to two sides and the in. duiled angle of the other ; therefore, the side AC is equa\ to BD (Prop. VI.), and the angle ACB...
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