 | Horatio Nelson Robinson - Conic sections - 1865 - 474 pages
...(Ax. 5). Hence the theorem ; the difference between any two sides of a triangle, etc. THEOREM XXI. jf two triangles have the three sides of the one equal to the three sides of the .other, each to each, the two triangles are equil, and the equal angles are opposite the equal sides. la two... | |
 | Charles Davies, William Guy Peck - Mathematics - 1865 - 592 pages
...need the following, which have been before proved, viz : Prop X. (of Legendre). " When two triansles have the three sides of the one equal to the three sides of the other, each to each, the three angles will also be equal, each to each and the triangles themselves will bo... | |
 | Benjamin Greenleaf - Geometry - 1866 - 328 pages
...equal to it ; hence the angle A must be greater than the angle D. PROPOSITION XVIII. — THEOREM. 80. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles themselves will be equal. Let the triangles ABC, DEF have the side AB equal... | |
 | Charles Davies - Mathematics - 1867 - 186 pages
...proposition, we need the following, which have been before proved ; viz. : Prop. X. (of Legendre). "If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles will be equal in all their parts." Prop. V. " If two triangles have two... | |
 | C. Davies - 1867 - 342 pages
...EAD will be equal to the angle KFor, draw the chord DE- Then the two triangles IKL and EAD, having the three sides of the one equal to the three sides of the other, each to each, the angle EAD will be equal -o the angle K (Bk- I- Th- viii)PROBLEM IXThrough a g1ven... | |
 | James Maurice Wilson - Geometry - 1868 - 132 pages
...one triangle can be constructed so as to have its sides equal to three given lines, it is clear that if two triangles have the three sides of the one equal to the three sides of the other, these triangles must be identical, or be equal in all respects. And a similar remark may be made on... | |
 | Education - 1868 - 516 pages
...similarity to those of the other. " — Campbells Rhet. This structure is very often neglected. Examples : "If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles will be equal in all their parts." The article before one here is improper,... | |
 | Edward Brooks - Geometry - 1868 - 284 pages
...AB. If it falls upon AB, the theorem is true by A. 7. Therefore, if two triangles, etc. THEOREM IX. If two triangles have the three sides of the one equal to the, three sides of the other, each to each, the triangles will be equal in all their parts. Let ABC and DEF be two triangles, having... | |
 | James Maurice Wilson - Geometry - 1868 - 150 pages
...are therefore equal. And if the chord AB is given equal to the chord PQ, then the triangles AOB, POQ have the three sides of the one equal to the three sides of the other; and therefore the angle AOB=\he angle POQ; and therefore also the arc AB = the arc PQ. COR. 1. If the... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...coincide throughout (Art. 34, Ax. 14). Thus circles having equal radii are equal ; and triangles having the three sides of the one equal to the three sides of the other, each to each, are also equal. Equal figures are always similar ; but similar figures may be very unequal.... | |
| |
If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent. 
