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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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'... "
An Elementary Treatise on Plane and Solid Geometry - Page 146
by Benjamin Peirce - 1871 - 150 pages
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 pages
...proportional sides are equal. VI. 23, cor. 1. VI. 23, cor. 2. VI. 19. . . VI. 15. VI. 19, cor. HYPOTHESES. If triangles have an angle of the one equal to an angle of the other. If triangles are equiangular . If triangles are similar . . If equal triangles have an angle of the...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 443 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
...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...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 520 pages
...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...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 320 pages
...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...
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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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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863
...reciprocalla proportional (tbat is, DB is to BE aŤ 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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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1865 - 186 pages
...AB C = PA C + PB C — PAB, and the triangle DEF = QDF -j- QEF— QDE ; whence the triangle ./iBC = the triangle DEF. ' * Area of a Spherical Triangle....supplements of those which include it in the other triangle ; the sum of the surfaces of the two triangles is measured by double the included angle. Proof....
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1869 - 182 pages
...a Spherical Triangle. are equilateral or equiangular with respect to each other, are equivalent. JC 468. Lemma. If two spherical triangles have an angle...supplements of those which include it in the other triangle ; the sum of the surfaces of the two triangles is measured by double the included angle. Proof....
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...the three sides of a triangle to the opposite angles meet in the same point. 14. If two trapezinms have an angle of the one equal to an angle of the other, and if, also, the sides of the two figures, about each of their angles, be proportionals, the remaining...
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