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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. "
Principles of Plane Geometry - Page 13
by James Wallace MacDonald - 1889 - 63 pages
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Annual Report

Canada. Department of the Interior - 1888 - 756 pages
...remains. Find the sum of money. No. of Marks. 7 5 i 8 8 8 8 8 11 11 [PART n] GEOMETRY. Time, 3 hours. 1. If two triangles have the three sides of one equal...three sides of the other, each to each, the triangles shall be eqnal in all respects. 2. Parallelograms on equal bases and between the same parallels are...
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Principles of Plane Geometry

James Wallace MacDonald - Geometry - 1894 - 76 pages
...equiangular triangle? 59. What is the hypotenuse of a right triangle? a. What are the other sides called ? 60. When are triangles equal? Equivalent? a. What...triangles are equal. Proposition XXIX. A Problem. 66. Construct an equilateral triangle having sides equal each to a given line. Proposition XXX. A Problem....
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Treatise on Trigonometry ...

William Ernest Johnson - Plane trigonometry - 1889 - 574 pages
...in all respects; so that BS '= AS. Similarly CS= AS, .'. BS = CS. .'. the triangles BDS, CDS having the three sides of one equal to the three sides of the other, are equal in all respects. .". DS is at right-angles to BC. Since AS, BS, CS are equal to one another,...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...well to learn the enunciation in the subjoined form : — If two triangles have the three sides of the one equal to the three sides of the other, each to each, then the triangles are identically equal, and of the angles, those are equal which are opposite to...
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry, Modern - 1891 - 428 pages
...equal. The triangles P AC and QDE are, then, isosceles triangles, and they have the three sides of the one equal to the three sides of the other, each to each. The same is true of the triangles PAB and QDF; and, also, of PBC and 0 F E. The corresponding isosceles...
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry, Modern - 1891 - 422 pages
...being any two triangles, etc. PROPOSITION III. 124. Theorem : If two triangles have three sides of the one equal to the three sides of the other, each to each, they are equal in all their parts. A Statement : Let the two triangles ACB and H FE have the side AC...
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Rider Papers on Euclid (books I. and II.)

Rupert Deakin - Euclid's Elements - 1891 - 102 pages
...Examinations, 1890. For Commercial Certificates. 1. If two triangles have three sides of the one equal to three sides of the other each to each, the triangles are equal to one another in every respect. Prove that the diagonals of a rhombus bisect one another, and cut...
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The Sewanee Review, Volume 4

American fiction - 1895 - 540 pages
...would a verse of poetry. Let us now consider another form of the proof. 282 The Sewanec Review. of the one equal to the three sides of the other, each to each, therefore they are equal ; hence, the angle BCA, opposite the side AB, is equal to the angle CAE, opposite...
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Geometry in the Grammar School: An Essay ...

Paul Henry Hanus - Geometry - 1893 - 76 pages
...three lines determine only one triangle, and hence that all triangles having the three sides of the one equal to the three sides of the other each to each are equal. In early instruction then the presentation of a new subject, and of each new phase of a...
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Elements of Geometry

George Cunningham Edwards - Geometry - 1895 - 330 pages
...spherical triangle be given, the spherical triangle may be constructed. It follows that if two spherical triangles have the three sides of one equal to the three sides of the other, the spherical triangles will be superimposable or symmetrical, and so will have the angles as well...
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