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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.
Elements of Geometry and Trigonometry - Page 107
by Adrien Marie Legendre - 1852 - 432 pages

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

Cambridge univ, exam. papers - 1856 - 200 pages
...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...

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

Euclides - 1856 - 168 pages
...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...

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

Peter Nicholson - Cabinetwork - 1856 - 518 pages
...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...

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

Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...homologous sides proportional (D. 1, 2); consequently, the two equiangular triangles BA C, CUD, are similar figures. Cor. Two triangles which have two...third angles are then equal, and the two triangles are equian gular (BI, p. 25, c. 2.) Scholium. Observe, that in similar triangles, the homologous sides...

## Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1857 - 242 pages
...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...

## The Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...angle in each, contained by proportional sides, are similar to each other. Any two triangles having two angles of the one equal to two angles of the other, are similar triangles, because the three angles of the one triangle are equal to the three angles of the other...

## Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858 - 248 pages
...demonstration of the following propositions. PROP. 26.— THEOR. — (Important.) 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., either the sides adjacent to the equal angles in...

## Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...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...