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" If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent. "
The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ... - Σελίδα 30
των Alexander Ingram - 1799 - 351 σελίδες
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Elements of geometry and mensuration

Thomas Lund - 1854 - 192 σελίδες
...CoR. Hence, also, the difference between any two sides is less than the third side. 39. PROP. XVII. If two triangles have two angles of the one equal to two angles of the other, each to each, and likewise the side which is common to those angles in the one equal to the side which is common to the...

Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - 1854 - 432 σελίδες
...consequently, the two equiangular triangles BAC, CED, are similar figures. Cor. Two triangles which have two angles of the one equal to two angles of the other, are similar ; for, the third angles are then equal, and the two triangles are equian gular (BI, p....

The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...Therefore, if two triangles, &c. QED The enunciation of this proposition may be thus simplif'ed: If two triangles have two angles of the one, equal to two angles of the other, each to each, and a side of the one equal to a side of the other similarly situated as to the equal angles, the two triangles...

The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855
...the angle EBC (4): and the angle AEG is equal to the angle BEH (a); therefore the triangles AEG, BEH have two angles of the one, equal to two angles of the other, each to each, and the sides AE, EB, adjacent to the equal angles, equal to one another; wherefore they have their other...

Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855
...drawn to intersect one another, the greater segments will be equal to the sides of the pentagon. 3. If two triangles have two angles of the one equal to two angles of the other, and one side equal to one side, viz. either the sides adjacent to the equal angles in each, or the...

Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 318 σελίδες
...it is not equal to it: therefore the angle BAC is greater than the angle EDF. PROP. XXVI. THLOR. Jf two triangles have two angles of the one equal to two angles of the otIirr, each to each; and one side equal to one side, viz. either the sides adjacent to the equal anglrs,...

Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...opposite angles are equal, these straight lines are, two and two, in the same straight line. 3. If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. the sides adjacent to equal angles in each; then shall the other sides...

Practical carpentry, joinery, and cabinet-making [by P. Nicholson. by P ...

Peter Nicholson - 1856 - 216 σελίδες
...parallel to CD, the alternate angles, GFE, FGH, are also equal ; therefore the two triangles GEF, HFG, have two angles of the one equal to two angles of the other, each to each ; and the side FG, adjacent to the equal angles, common ; the triangles are therefore equal (theorem 6) ;...

The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...BAC, and the angle ABE is equal to the angle ABC (being both right angles), the triangles ABC, ABE have two angles of the one equal to two angles of the other, and the side AB common to the two. Therefore the triangles ABC, ABE are equal, and the side AE is equal...

Elements of Geometry and Conic Sections

Elias Loomis - 1857 - 226 σελίδες
...is parallel to CD, the alternate angles GHE, HEF are also equal. Therefore, the triangles HEF, EHG have two angles of the one equal to two angles of the other, each to each, and the side Eli included between the equal angles, common ; hence the triangles are equal (Prop. VII.)...




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