 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 48by Thomas Hunter - 1878 - 132 pagesFull view - About this book
 | Elias Loomis - Conic sections - 1861 - 244 pages
...right angles. PROPOSITION VI. THEOREM. If two triangles have two sides, and the included angle of t/ie one, equal to two sides and the included angle of the other > each to each, the two triangles will be equal, their third sides will be equal, and their other angles will be equal,... | |
 | Benjamin Greenleaf - Geometry - 1862 - 514 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... | |
 | Benjamin Greenleaf - Geometry - 1861 - 628 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... | |
 | Benjamin Greenleaf - Geometry - 1862 - 520 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... | |
 | 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... | |
 | 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,... | |
 | Charles Davies - 1863 - 424 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 - 330 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
...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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