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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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School Algebra

William Ernst Paterson - Algebra - 1908 - 604 pages
...are equiangular, the ratios of corresponding aides are equal. Theorem III. If two triangles have one angle of the one equal to an angle of the other and the aides about the equal angles proportional, then' the triangles are equiangular. 237. Theorem I leads...
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Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...to two angles of the other. PROPOSITION XVIII. THEOREM. 368. Two triangles are similar if they have an angle of the one equal to an angle of the other and the including sides proportional. EF Given As ABC and DBF in which XA = XD, and — = — . DE DF To prove...
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 300 pages
...similar triangles ACD and EBC that AC- BC = CE- CD. 430. EXERCISES. 1. The areas of two parallelograms having an angle of the one equal to an angle of the other are in the same ratio as the product of the sides including the equal angles. 2. Three semicircles...
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 304 pages
...similar triangles ACD and EBC that AC- BC= CE- CD. 430. EXERCISES. 1. The areas of two parallelograms having an angle of the one equal to an angle of the other are in the same ratio as the product of the sides including the equal angles. 2. Three semicircles...
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Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...interior angles is equal to four times the sum of its exterior angles ? Ex. 82. If two parallelograms have an angle of the one equal to an angle of the other, they are mutually equiangular. Ex. 83. A parallelogram is divided into two congruent parts by a line...
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Wentworth's Plane Geometry

George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...ZA=ZA'. 282 AABC ABX.AC Then rTT , = , , —— • 332 (The areas of two triangles that 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.) AABC AB AC 1S, A t'fi'C'...
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Elementary Trigonometry

William Ernst Paterson - Logarithms - 1911 - 204 pages
...and a side of the one equal to the corresponding side of the other. Prop. 9. If two triangles have an angle of the one equal to an angle of the other, and the sides about another pair of angles equal, each to each, then the third angles are either equal or supplementary....
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College Entrance Examination Papers in Plane Geometry

Geometry, Plane - 1911 - 192 pages
...equal, respectively, to adjacent sides and the included angle of the other. 3. Prove that 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. 6. Prove that a line perpendicular...
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Plane Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 303 pages
...that the triangle ODC is equilateral. Ex. 924. Assuming that 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, prove that the bisector...
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The Teaching of Geometry

David Eugene Smith - Geometry - 1911 - 339 pages
...tape, is given on page 99. THE TEACHING OF GEOMETRY THEOREM. 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. This proposition may be...
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