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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. If two right-angled triangles have their hypotenuses equal, and one side of the one equal to one side of the other, the... "
The Bombay University Calendar - Page 59
by University of Bombay - 1906
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Elementary Illustrations of the Celestial Mechanics of Laplace: Part the ...

Pierre Simon marquis de Laplace, Thomas Young - Capillarity - 1821 - 402 pages
...ABC; therefore ABC=DEF, and the angles at A and B are equal to the angles at D and E. 87. THEOREM. If two sides of a triangle are equal, the angles opposite to them are equal. In the sides AB and AC produced, take at pleasure AD=AE, and join BE, CD; then since...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856 - 168 pages
...angles will be equal or unequal, or which of them will be the greater; but geometry teaches us, that if two sides of a triangle are equal, the angles opposite to the equal sides are also equal to each other; and if the sides are unequal, the angle which is opposite...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1857 - 242 pages
...angle BAC must be greater than the angle EDF. Therefore, if two triangles, &c. PROPOSITION XV. THEOREM. If two triangles have the three sides of the one equal to tne three sides of the other, each to each, the three angles will also '• be equal, each to each,...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...angle BAC must be greater than the angle EDF. Therefore, if two triangles, &c. PROPOSITION XV. THEOREM. If two triangles have the three sides of the one equal to trie three sides of the other, each tc each, the three angles will also be equal, each to each, and...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Geometry - 1860 - 468 pages
...; when two triangles have a side and two adjacent angles in the one, equal to, etc. THEOREM XVIII. If two sides of a triangle are equal, the angles opposite to these sides are also equal. Let ABC be a triangle ; and on the supposition that AC = BC, we are to prove that the [_...
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Elements of plane geometry, book i, containing nearly the same propositions ...

Euclides - 1865 - 80 pages
...to the angle EAF, and the angle BAC is bisected by the straight line AF. E PROPOSITION XIV. TIIEOR. If two sides of a triangle are equal, the angles opposite to them are also equal. In the triangle ABC, let the side AB be equal to the side AC, then the angle B...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 pages
...angle BAC must be greater than the angle EDF. Therefore, if two triangles, &c. PROPOSITION XV. THEOREM. If two triangles have the three sides of the one equal to trie '.hree sides of the other, each to each, the three angles will also be eqi. il, each to each,...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1880 - 452 pages
...BAC must be greater than the angle EDF. Therefore, if two triangles, etc. PROPOSITION XV. THEOREM. If two triangles have the three sides of the one equal to the threo sides of the other, each to each, the three angles will also be equal. each to each, and the...
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883 - 86 pages
...of the sides those are equal which are opposite to the equal angles. [By Superposition.] THEOR. 7. If two sides of a triangle are equal, the angles opposite to those sides are equal. [By a single application of Theor. 5, or directly by Superposition.] COR. If...
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The elements of plane geometry, Volume 1

Mathematical association - 1884 - 146 pages
...angle of a triangle is also perpendicular to the opposite side, the triangle is isosceles. THEOB. 7. If two sides of a triangle are equal, the angles opposite to those sides are equal. Let ABC be a triangle having the side AB equal to the side AC: then shall the...
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