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" If two triangles have an angle of one equal to an angle of the other... "
Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Σελίδα 172
των Euclid, Rev. John Allen - 1822 - 494 σελίδες
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The Teaching of Geometry

David Eugene Smith - 1911 - 339 σελίδες
...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 omitted as far as...

College Entrance Examination Papers in Plane Geometry

1911 - 178 σελίδες
...vertices of a parallelogram. When will this parallelogram be a rectangle? 2. Prove that if two triangles have an angle of one equal to an angle of the other, and the sides including these angles proportional, the triangles are similar. Prove that if two diagonals...

Solid Geometry

Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - 1912 - 188 σελίδες
...circle is equal to one half its perimeter multiplied by the radiue of the inscribed circle. 498. Two triangles which have an angle of one equal to an angle of the other are to each other as the products of the sides including the equal angles. 503. Two similar triangles are to each other...

Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - 1912 - 332 σελίδες
...measurements being in centimeters. f? . J/r IJ t T' y, d ' i d PROPOSITION IV. THEOREM 337. If two triangles have an angle of one equal to an angle of the other, their areas are to each other as the products of the sides including the equal angles. c' zc Given...

Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - 1912 - 332 σελίδες
...44, 36, 28, and 20, measurements being in centimeters. PROPOSITION IV. THEOREM 337. If two triangles have an angle of one equal to an angle of the other, their areas are to each other as the products of the sides including the equal angles. Given two triangles...

Plane and Solid Geometry

Clara Avis Hart, Daniel D. Feldman - 1912 - 488 σελίδες
...of two given circles. Ex. 1125. 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 of an angle of a triangle...

Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - 1913 - 457 σελίδες
...PLANE GEOMETRY 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 products of the sides including the equal angles. Given A ABC and A'B'C', ZA = Z A'. To prove...

Schultze and Sevenoak's Plane Geometry

Arthur Schultze, Frank Louis Sevenoak - 1913 - 304 σελίδες
...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 A = ZA ' . To prove...

Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - 1913 - 470 σελίδες
...ft, 9 ft., 5 ft. PROPOSITION VII. THEOREM 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. •A. DB Given the triangles ABC and ADE,...

Constructive Text-book of Practical Mathematics

Horace Wilmer Marsh, Annie Griswold Fordyce Marsh - 1914
...triangle are in what relation to the angles of the greater triangle? Finish the demonstration. V THEOREM 5 Triangles which have an angle of one equal to an angle of the other and the including sides proportional are similar. By what theorems have triangles been proved similar?...




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