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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 - Page 65
by Adrien Marie Legendre - 1841 - 235 pages
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 514 pages
...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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Primary Elements of Plane and Solid Geometry: For Schools and Academies

Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...to DGE : 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 to the...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 320 pages
...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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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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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865
...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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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1868 - 338 pages
...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, PEF have the angle A...
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Catalogue of the Officers and Students

Trinity College (Hartford, Conn.) - 1870
...intercepted arc. 3. Two triangles are similar when they are mutually equiangular. 4. Two triangles having 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. 5. What is the length of...
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The Elements of Plane and Solid Geometry

Henry William Watson - Geometry - 1871 - 285 pages
...AGH, therefore the triangle ABC is similar to the triangle DEF. PROPOSITION 18. If two triangles have an angle of the one equal to an angle of the other, and the sides containing those angles proportionals, the triangles shall be similar. Fig. 25. Let ABC and DEF be...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...square of the ratio of similitude of the triangles. PROPOSITION VIII— THEOREM. 22. Two triangles having 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. Two triangles which have...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 238 pages
...equiangular (I. 35^, and similar (20) ; therefore BG:EH—AB:DE=AC:DF=BC:EF THEOREM X. 23, Two triangles having an angle of the one equal to an angle of the other, and the sides including these angles proportional, are similar. E D In the triangles ABC, DEF let t!:e angle A =...
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