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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 Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...angle EBC: and the angle AEG is •15.1. equal* to the angle BEH: 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: • 26. 1....

## The Complete Mathematical and General Navigation Tables: Including ..., Volume 1

Thomas Kerigan - Nautical astronomy - 1828 - 776 pages
...opposite angle CBF, — Euclid, Book I., Prop. 29. And, since the two triangles AFD and FBC have, thus, two angles of the one equal to two angles of the other, viz., the angle AFD to the angle FBC, and the angle FAD to the angle BFC, and the side AF of the one...

## Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 228 pages
...mO' and M'N'O' are equal. The angle N'O'M' is common to the two triangles nmO' and N'M'O'; and having two angles of the one equal to two angles of the other, the other angles must be equal, that is, the angle O'M'N' is equal to the angle O' nm ; and this intersection...

## Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...equal to the arc В С (12.); therefore the angle В О a is equal to BO b. Therefore BO a, BO b are triangles which have two angles of the one equal to two angles of the other, each to each, and the interjacent side О В common to both : consequently, (I. 5.) they are equal...

## Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...be proved in all other triangles under the same conditions. Wherefore, universally, if two triangles have two angles of the one, equal to two angles of the other respectively ; &c. Which was to be demonstrated. PROPOSITION XXVII. THEOREM. — If a straight line...

## The Moral Class Book, Or The Law of Morals: Derived from the Created ...

William Sullivan - Ethics - 1833 - 380 pages
...it. It is a truth, for example, but not a self-evident one, that if one draw two triangles, having two angles of the one equal to two angles of the other, each to each ; and one side equal to one side, viz. either of the sides adjacent to the equal angles,...

## The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...and the right angle FHC equal to the right angle FKC, therefore in the triangles FHC, FKC there are two angles of the one, equal to two angles of the other, each to each ; and the side FC, which is opposite to one of the equal angles in each, is common to...

## Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...the arc В С (12.); therefore the angle В О a is equal to BO b. Therefore В О а, В О b are triangles which have two angles of the one equal to two angles of the other, each to each, and the interjacent side О В common to both : consequently, (I. 5.) they are equal...