Books Books 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 48
by Thomas Hunter - 1878 - 132 pages ## Psychology, Or, Elements of a New System of Mental Philosophy: On the Basis ...

Samuel Simon Schmucker, S. S. (Samuel Simon) Schmucker - History - 1855 - 332 pages
...the nature, eg, of the demonstration of the theorem of Euclid known as Prop. IV. of Book I., viz.: If two triangles have two sides, and the included angle...the one equal to two sides and the included angle of the other, they must be identical or equal in all respects. For it virtually consists in supposing... ## The Quarterly Journal of Pure and Applied Mathematics, Volume 7

Mathematics - 1866 - 426 pages
...his Demonstration of I. G anything else ? by supposing BG = AC. he obtains two triangles having two sides and the included angle of the one equal to two sides and the included angle of the other ; two triangles, which, if the supposition BG = AG is correct should, applied one upon... ## Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1855 - 630 pages
...themselves will bo equal." Prop. V. " When two triangles have two sides, and the included angle of the une equal to two sides and the included angle of the other, each to each, the two triangles will be equal. "Axiom 1. Things which are equal to tho same thing are equal to each... ## Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...line which has the sum of the interior angles less than two right angles. OF TRIANGLES. THEOREM XX. If two triangles have two sides and the included angle of the one, equal to the two sides and the included angle of the other, the triangles will fie identical, or equal in all... ## Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1857 - 444 pages
...by construction, AG=DE: DF, Q D B AH. CEP DF; hence AH=DF. Therefore, the two triangles A GH, DEF, have two sides and the included angle of the one equal to two sides and the included angle of the other : hence, they are equal (BI, p. 5) ; but the triangle A GH is similar to ABC : therefore,... ## Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1857 - 242 pages
...because AB is equal to CD, and BC is common to the two triangles ABC, BCD, the two triangles ABC, BCD have two sides and the included angle of the one, equal to two sides and the included angle of the other ; therefore, the side AC is equal to BD (Prop. VI.), and the angle ACB to the angle CBD.... ## Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...because AB is equal to CD, and BC is common to the two triangles ABC, BCD, the two triangles ABC, BCD have two sides and the included angle of the one, equal to two sides and the included angle oi the other ; therefore, the side AC is equal to BD (Prop. VI.), and the angle ACB to the angle CBD.... ## Carpentry Made Easy: Or, The Science and Art of Framing, on a New and ...

William E. Bell - Bridge building - 1857 - 254 pages
...FAGE is equivalent to the square P. Again, the two triangles ABH rod CBI are equal, having also two sides and the included angle of the one equal to two sides and the included angle of the other ; and AHB is half of 'he square X, and CBI is half of the rectangle FBIG : therefore,... ## Carpentry Made Easy, Or, The Science and Art of Framing, on a New and ...

William E. Bell - Bridges - 1859 - 224 pages
...two quantities ; 8; AXS:BX8:: A:B; (AX8)XB=(BX8)XA, AX8:BX8::A:B. Proposition VIII. Theorem. Wlien two triangles have two sides and the included angle...the one equal to two sides and the included angle of tJn other, each to each, the two triangles are equal. 1n the triangles ABC and DEF, let AB=DE, AC=DF,... 