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" Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional ; and parallelograms that have one angle of the one equal to one angle of the other, and their sides... "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Page 94
by Dennis M'Curdy - 1846 - 138 pages
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Plane Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 332 pages
...will be a parallelogram equal in area to half the original figure. PROPOSITION VIII. THEOREM 498. Turn triangles which have an angle of one equal to an angle of the otlier are to each other as the products of tlie sides including the equal angles. Given A AliC and...
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The Dublin University Calendar, Volume 1

Trinity College (Dublin, Ireland) - 1911 - 616 pages
...triangles are equiangular. 10. Prove that equal parallelograms which have one angle of the one equal to one angle of the other have their sides about the equal angles reciprocally proportional. ALGEBRA AMD ARITHMETIC. MR. WEBB. 1 . Find the common factor of 2z4 + (>& - lye* + 3 - 7 and $%*...
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Secondary-school Mathematics, Volume 2

Robert Louis Short, William Harris Elson - Mathematics - 1911 - 216 pages
...lines; areas are in the same ratio as squares of homologous THEOREM LVII 213. Two triangles having an angle of one equal to an angle of the other have the same ratio as the products of the sides including the equal angles. Draw A ABC and DEF having ZA...
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Solid Geometry

Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - Geometry, Solid - 1912 - 216 pages
...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...
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Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Modern - 1912 - 360 pages
...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...
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Plane Geometry

William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...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...
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The Dublin University Calendar, Volume 1

Trinity College (Dublin, Ireland) - 1913 - 568 pages
...the angle ASC is equal either to the angle AGP or to the angle ACQ. 7. Prove that if two triangles have an angle of one equal to an angle of the other, and the sides about these equal angles proportional, they are similar. 8. Prove that similar polygons...
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Constructive Text-book of Practical Mathematics, Volume 2

Horace Wilmer Marsh, Annie Griswold Fordyce Marsh - Mathematics - 1914 - 270 pages
...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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Solid Geometry

Sophia Foster Richardson - Geometry, Solid - 1914 - 234 pages
...if they are mutually equiangular ; (6) if their corresponding sides are proportional ; (c) if they have an angle of one equal to an angle of the other and the including sides proportional. 249. Show that two plane polygons can be placed in the homothetic...
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Examination Questions in Mathematics: Third Series, 1911-1915

College Entrance Examination Board - Mathematics - 1915 - 60 pages
...locus. Find the locus of the center of a circle passing through two given points. 3. The areas of two triangles which have an angle of one equal to an angle of the other are to each other as the products of the side including those angles. 4. Construct a triangle ABC;...
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