 | Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...triangles be 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,... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...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... | |
 | 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,... | |
 | 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... | |
 | 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... | |
 | Euclides - 1865 - 80 pages
...angles being always opposite to the equal sides. PROPOSITION XII. TIIEOR. If two triangles have two sides, and the included angle of the one equal to...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,... | |
 | Education - 1866 - 446 pages
...the morrow, to be that starting point in the properties of triangles, viz : If two triangles have two sides and the included angle of the one equal to two....and the included angle of the other, each to each, the two triangles will be equal in every respect. The teacher draws the diagram on the board, and desires... | |
 | Charles Davies - Mathematics - 1867 - 186 pages
...each to each, the triangles will be equal in all their parts." Prop. V. " If two triangles have two sides and the included angle of the one, equal to...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,... | |
 | C. Davies - 1867 - 342 pages
...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... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...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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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 in all their parts." Axiom 1. "Things which are equal to the same thing, are equal... 
