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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 will be equal. "
Elements of Geometry and Conic Sections - Page 17
by Elias Loomis - 1857 - 226 pages
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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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The Normal Elementary Geometry: Embracing a Brief Treatise on Mensuration ...

Edward Brooks - Geometry - 1868 - 284 pages
...but EGB equals D.EF, being alternate ; hence, ABC equals DEF. Therefore, etc. TRIANGLES. THEOREM VI. If two triangles have two sides and the included angle...the included angle of the other, each to each, the triangles will be equal in all their parts. Let the triangles ABC and DEF have the side AB equal to...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1868 - 340 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 - 170 pages
...other ? 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 of the other, each to each, the two triangles are equal in all respects. Let the triangles abe and d ef have the side ab of the one equal to the...
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Marks' First Lessons in Geometry: Objectively Presented

Bernhard Marks - Geometry - 1869 - 180 pages
...other? 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...and the included angle of the other, each to each, tlie two triangles are equal in all respects. Let the triangles abc and d ef have the side ab of the...
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Marks' First Lessons in Geometry: Objectively Presented

Bernhard Marks - Geometry - 1869 - 172 pages
...the angle ADC. Therefore the angle AB c is equal to the angle ADC. Then the two triangles AB c, AD c, have two sides, and the included angle of the one...and the included angle of the other, each \ to each, and are equal in all their parts ; that is, the three angles of the one are equal to the three angles...
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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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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
...the angle ADC. Therefore the angle AB c is equal to the angle ADC. Then the two triangles AB c, AD c, have two sides, and the included angle of the one...and the included angle of the other, each to each, and are equal in all their parts ; that is, the three angles of the one are equal to the three angles...
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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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