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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. "
Elements of Geometry: With Practical Applications to Mensuration - Page 59
by Benjamin Greenleaf - 1863 - 320 pages
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Elements of Geometry and Trigonometry;: With Practical Applications

Benjamin Greenleaf - Geometry - 1863 - 502 pages
...Conversely, if the chord AD is equal to the chord EG, the arcs AD, EG will be equal. For, if the radii CD, OG are drawn, the triangles ACD, E 0 G, having the three...semicircle ADB be applied to its equal EGF, with the radius A0 on its equal E0, since the angles ACD, E 0 G are equal, the radius CD will fall on OG, and the point...
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Elements of Geometry and Trigonometry

C. Davies - 1867 - 342 pages
...the angle 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...
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Outlines of Mathematical Science for the School Room

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...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - 1868 - 338 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...
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Elementary Geometry, Volume 2

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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Marks' First Lessons in Geometry: Objectively Presented

Bernhard Marks - Geometry - 1869 - 170 pages
...side A B. 'D It 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...
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Elements of Geometry, Plane and Spherical: With Numerous Practical Problems

Horatio Nelson Robinson - 1869 - 276 pages
...ED = 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, each to each; therefore, the two A's are equal, (Th. 21). If, from the whole figure ABDC, we take away the A CAF,...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1870 - 319 pages
...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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Marks' First Lessons in Geometry: In Two Parts : Objectively Presented and ...

Bernard Marks - Geometry - 1871 - 172 pages
...ILLUSTRATED. 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 part's. Let the two triangles ABC, ADC, have the side AB of the one equal...
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Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871
...triangle be.equal, the sides wMch tubtend them are also equal. (Eucl. i. 6.) SE 2 If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles must be equal in all respects. -25 q _ Let the three sides of the A s ABO, DEF be equal,...
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