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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

The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...the right angle BED is equal to the right angle BFD ; the two triangles EUCLID 8 ELEMENTS. EBD, FBD have two angles of the one equal to two angles of the other ; and the side BD, which is opposite to one of the equal angles in each, is common to both ; therefore...

The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 176 pages
...bisected by Ь d, and that the right angle bed is equal to the right angle bfd, the two triangles ebd, fbd have two angles of the one equal to two angles of the other, and the side bd, which is opposite to one of the equal angles in each, is common to both ; therefore...

The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pages
...the right angle BED is equal (Ax. 11.) to the right angle BFD; therefore the two triangles EBD, FBD, have two angles of the one equal to two angles of the other, each to each , and the side BD, which is opposite to one of the equal angles in each, is common to...

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

Charles Davies - Geometry - 1854 - 436 pages
...homologous sides proportional (D. 1, 2); consequently, the two equiangular triangles BAC, CED, 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...

The popular educator, Volume 4; Volume 7

Popular educator - 1852 - 1272 pages
...triangles, &c. QED Scholium. The enunciation of this proposition may be thuğ simplified : If two triangles have two angles of the one, equal to two angles of the other, each to each, and u side of the one equal to a side of the other similarly situated as to the equal...

Elements of geometry and mensuration

Thomas Lund - Geometry - 1854 - 520 pages
...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...

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

Robert Potts - 1855 - 1050 pages
...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...

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

Euclides - 1855 - 270 pages
...and the right angle BED (I. Ax. 11) to the right angle BF D. Therefore the two triangles EBD and FBD have two angles of the one equal to two angles of the other, each to each ; and the side BD, which is opposite to one of the equal angles in each, is common to...