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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 Plane Geometry: For the Use of Schools - Page 71
by Nicholas Tillinghast - 1844 - 96 pages
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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
...Given .-. 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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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 304 pages
...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 - 300 pages
...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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Elementary Trigonometry

William Ernst Paterson - Logarithms - 1911 - 266 pages
...each, 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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The Teaching of Geometry

David Eugene Smith - Geometry - 1911 - 358 pages
...the use of pupils who may be working only with the tape, is given on page 99. 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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Plane Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 328 pages
...the radii OD and OO. Prove 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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College Entrance Examination Papers in Plane Geometry

Geometry, Plane - 1911 - 192 pages
...becomes when one of these latter two sides is perpendicular to the other. 7. Prove 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 enclosing the equal angles. B 8. The lines joining successively...
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Plane Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry, Modern - 1911 - 266 pages
...equivalent to the sum of three given squares. PROPOSITION XV. THEOREM 369. The areas of two triangles ivhich 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 A' Hyp. In triangles ABC...
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Schultze and Sevenoak's Plane Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...two given squares. [The solution is left to the student.] PROPOSITION XIII. THEOREM 378. 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 product of the sides including the equal angles. Given A ABC and A'B'C', Z...
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