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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, containing the first six books, with a selection of ... - Σελίδα 23
των Euclides - 1874
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## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 σελίδες
...by BD, and because 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 Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - 1835 - 513 σελίδες
...equal to KCF, and the right angle FHC equal to the right angle FKC; in the triangles FHC, FKC there are two angles of the one equal to two angles of the other, and the side FC, which is opposite to one of the equal angles in each, is common to both : therefore...

## The Element of Geometry

John Playfair - 1836 - 114 σελίδες
...bisected by BD, and that the right angle BED is equal to the right angle BFD, the two Iriangles 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...

## Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - 1837 - 246 σελίδες
...SECTION IV. two angles of the one is equal to the sum of the remaining two angles of the other. 2. If two triangles have two angles of the one equal to two angles of the other, each to each, the third angle of the one is equal to the third angle of the other ; that is, the triangles are equiangular....

## Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - 1837 - 254 σελίδες
...and if the equal angles be subtracted from these equals, the remaining angles must be equal. M.—If two triangles have two angles of the one equal to two angles of the other, each to each, what may be said of the remaining third angles ? P.—They must be equal,—for the reason alleged...

## The mechanical Euclid, containing the elements of mechanics and hydrostatics

William Whewell - 1837 - 226 σελίδες
...angle; therefore MLN is equal to LKH; and the angles at H and at N are right angles. Therefore the triangles have two angles of the one equal to two angles of the other ; and the side KL is equal to LM. Therefore the triangles are equal, and HL is equal to MN; that is,...

## Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 σελίδες
...by BD ; and because 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 First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 410 σελίδες
...is equal (const.) to FBD, and that the right angles BED, BFD are equal, 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...

## Solid and Spherical Geometry and Conic Sections: Being a Treatise on the ...

A. Bell - 1837 - 180 σελίδες
...Def. 7)i and therefore the angles AFG, AEG, are also equal. The triangles AGE, AGF, have therefore two angles of the one equal to two angles of the other, and they have also the side AG common ; wherefore they are equal, and the side AF is equal to the side...

## Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 σελίδες
...that the <UAx. right angle BED is equalt 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, B Tf C •which is opposite to one of the equal angles in each, is common to both ; therefore...