 | Euclides - 1865 - 80 pages
...DEF, 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...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, AC to... | |
 | 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...other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other." Axiom... | |
 | 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... | |
 | 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... | |
 | 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.... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | Richard Wormell - Geometry, Plane - 1870 - 304 pages
...greater is greater than the angle opposite the less (ยง76). 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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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. 
