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" The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw... "
Elements of Geometry and Trigonometry Translated from the French of A.M ... - Page 82
by Charles Davies - 1849 - 359 pages
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1857 - 242 pages
...triangles, &c. PROPOSITION XX. THEOREM. Two triangles are similar, when they have an angle of the une equal to an angle of the other, and the sides containing those angles proportional. Let the triangles ABC, DEF have the angle A of the one, equal to the angle D of the other, and let...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 252 pages
...the triangles PROPOSITION XX. THEOREM. Two triangles are similar, when they have an angle of the une equal to an angle of the other, and the sides containing those angles proportional. Let the triangles ABC, DEF have the angle A of the one, equal to the angle D of the other, and let...
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Manual of Euclid: books iv., v., vi., by J.A. Galbraith and S. Haughton

Euclides - 1859 - 132 pages
...rpiywvwv, vriirtirvQaaiv at ir\tvpai, ai irepi r; ffa ywvia, laa iariv iKtlva. Equal triangles which have an angle of the one equal to an angle of the other have their sides about the equal angle* reciprocally proportional ; and triangles which have an angle...
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 pages
...If equal parallelograms have an angle of the one equal to an angle of the other. If parallelograms have an angle of the one equal to an angle of the other, and their sides about the equal angles reciprocally proportional. If parallelograms are about the diameter...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 468 pages
...other, and the sides containing the equal angles proportional. Two rhombuses are similar, when they have an angle of the one equal to an angle of the other. All squares are similar figures. All regular polygons of the same number of sides are similar figures....
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 514 pages
...properties of triangles include, by implication, those of all figures. PROPOSITION XXIV . — THEOREM. 264. Two triangles, which have an angle of the one equal...to an angle of the other, and the sides containing these angles proportional, are similar. Let the two triangles ABC, DEF have the angle A equal to KD...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 520 pages
...properties of triangles include, by implication, those of all figures. PROPOSITION XXIV. — THEOREM. 264. Two triangles, which have an angle of the one equal...to an angle of the other, and the sides containing. these angles proportional, are similar. Let the two triangles ABC, DEF have the angle A equal to the...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 506 pages
...properties of triangles include, by implication, those of all f1gures. PROPOSITION XXIV. — THEOREM. 264. Two triangles, which have an angle of the one equal...to an angle of the other, and the sides containing these angles proportional, are similar. Let the two triangles ABC, DEF have the angle A equal to the...
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863 - 118 pages
...angles reciprocalla proportional (tbat is, DB is to BE a GB /stoBF); and, converseln, parallelograms which have an angle of the one equal to an angle of the other, and their sides about the equalangles reciprocallg proportional, are equal to one another. Place the parallelograms...
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Primary Elements of Plane and Solid Geometry: For Schools and Academies

Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...: hence, it is also similar to DFE. Therefore, two triangles, etc. THEOREM V. Two triangles having an angle of the one equal to an angle of the other, and the sides about those angles proportional, are similar. Let the two triangles ABC, DEF, have the angle A equal...
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