 | Elias Loomis - 1861 - 244 Seiten
...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 - 1862 - 532 Seiten
...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 - 1861 - 638 Seiten
...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 - 1862 - 518 Seiten
...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 - 1863 - 504 Seiten
...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 - 1862 - 116 Seiten
...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 - 436 Seiten
...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, and... | |
 | Adrien Marie Legendre - 1863 - 464 Seiten
...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 - 1864 - 358 Seiten
...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... | |
 | Charles Davies - 1867 - 186 Seiten
...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...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,... | |
| |
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. 
