 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...are mutually equilateral, they are equivalent. ELEMENTS OF GEOMETRY. Let ABC, DEF be two triangles, having the three sides of the one equal to the three sides of the other, each to each, namely, AB to DE, AC to DF, andCBtoEF; then their triangles will be equivalent. Let 0 he the pole of... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...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, А С... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...hence the angle BAC is greater than ABC. PROPOSITION XVII. — THEOREM. Let ABC, DBF bo two triangles, having the three sides of the one equal to the three sides of the other, each to each, namely, AB to DE, F / ACtoDF, andCB toEF; then their triangles will bo equivalent. Let 0 be the pole... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...other, coincide throughout (Art. 84, 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. BOOK IV.... | |
 | Horatio Nelson Robinson - Conic sections - 1865 - 474 pages
...= CF, (Ax. 3) ; but BE = AC, and AF = BD, (Th. 24); hence we have two A's, CAF and EBD, which have the three sides of the one equal to the three sides of the other, e,ach to each; therefore, the two A's are equal, (Th. 21). If, from the whole figure ABDC, we take away the A CAF,... | |
 | Benjamin Greenleaf - Geometry - 1866 - 328 pages
...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 to... | |
 | C. Davies - 1867 - 342 pages
...chord IL, describe an arc cutting DE at D; draw AD, and the angle EAD will be equal to the angle KFor, draw the chord DE- Then the two triangles IKL and...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 a line that shall be parallel... | |
 | Charles Davies - Mathematics - 1867 - 186 pages
...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 included... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...greater 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... | |
 | James Maurice Wilson - Geometry - 1868 - 150 pages
...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... | |
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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. 
