 | Benjamin Greenleaf - 1866 - 328 σελίδες
...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 to DE, AC... | |
 | Charles Davies - 1867 - 186 σελίδες
...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 sides and the... | |
 | C. Davies - 1867 - 342 σελίδες
...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 point to draw... | |
 | Horatio Nelson Robinson - 1868 - 276 σελίδες
...from the whole line CD we take, in succession, CE and FD, there will remain ED = CF, (Ax. 3) ; \>ut BE = AC, and AF= BD, (Th, 24); hence we have two A's,...EBD, which have the three sides of the one equal to tho tb ree sides of the other, each to each ; therefore, the tvo A's are equal, (Th. 21). If, from... | |
 | 1868 - 516 σελίδες
...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, because the... | |
 | James Maurice Wilson - 1868 - 132 σελίδες
...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... | |
 | Benjamin Greenleaf - 1868 - 340 σελίδες
...than ABC. PROPOSITION XVII. — THEOREM. ELEMENTS OP GEOMETRY. Let ABC, DBF be two triangles, having the three sides of the one equal to the three sides of the other, eaeh to each, namely, AB to DE, AC toDF, andCB toEF; then their triangles will be equivalent. Let 0... | |
 | Horatio Nelson Robinson - 1869 - 276 σελίδες
...the theorem; the difference between any two sidei of a triangle, etc. THEOREM XXI. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the two triangles are equTl, and the equal angles are opposite the equal sides. In two triangles, as... | |
 | Bernhard Marks - 1869 - 172 σελίδες
...THEOREMS ILLUSTRATED. DB PROPOSITION XIX. THEOREM. DEMONSTRATION. We wish to prove that, If two triangles have the three sides of the one equal to the three sides of the other, each to each, they are equal in all their parts. Let the two triangles ABC, ADC, have the side AB of the one equal... | |
 | Charles Davies - 1870 - 392 σελίδες
...called a direct, and the latter an indirect demonstration. THEOREM via. If two triangles have tlie three sides of the one equal to the three sides of the other, each to each, the three angles will aho be equal, each to each. Let the two triangles ABC, ABD, have the side AB... | |
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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. 
