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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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Principles of Plane Geometry

James Wallace MacDonald - Geometry - 1889 - 63 pages
...the triangles are equal. Proposition XXVIII. A Theorem. 65. If two triangles have the three sides of one equal to the three sides of the other, each to each, the triangles are equal. Proposition XXIX. A Problem. Proposition XXX. A Problem. 67. Construct a triangle...
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Principles of Plane Geometry

James Wallace MacDonald - Geometry - 1894 - 76 pages
...the triangles are equal. Proposition XXVIII. A Theorem. 65. If two triangles have the three sides of one equal to the three sides of the other, each to each, the triangles are equal. Proposition XXIX. A Problem. 66. Construct an equilateral triangle having...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 pages
...The student would do 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 - 422 pages
...; AH is common, by construction ; and AB is equal to AC, by hypothesis. The two triangles have then the three sides of the one equal to the three sides of the other, each to each, and they are, therefore, equal. (PROP, in.) The corresponding parts being equal to each other, the...
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry, Modern - 1891 - 428 pages
...: / 2 3 and 456 being any two triangles, etc. PROPOSITION III. 134. 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. AS Statement: Let the two triangles A CB and HFE have the side AC...
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry - 1891 - 428 pages
...: / 2 3 and 456 being any two triangles, etc. PROPOSITION III. 134. Theorem : If two triangles have three sides of the one equal to the three sides of the other, each to cucli, they are equal in all their parts. Statement: Let the two triangles AC B and H FE have the side...
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The Sewanee Review, Volume 4

American fiction - 1895 - 542 pages
...he 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 - 52 pages
...of three wires, he sees that 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 subject,...
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Elements of Geometry

George Cunningham Edwards - Geometry - 1895 - 332 pages
...for another and may be made to occupy exactly B Fro. 24. TRIANGLES. THEOREM. If two triangles have the three sides of the one equal to the three sides of the other, each to each, they are congruent. If the two triangles (p) and (g) having : AB=DE, BC = DF, and AC=EF, be so placed...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1895 - 450 pages
...Therefore, if two triangles, etc. PROPOSITION XV. THEOREM. If two triangles have the three sides oftJie one equal to the three sides of the other, each to each, the three angles will also bc equal, each to each, and the triangles themselves will be equal. Let...
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