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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. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'. "
Plane Geometry - Page 180
by Arthur Schultze - 1901
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Elements of Plane Geometry

Franklin Ibach - Geometry - 1882 - 208 pages
...AD or AC* : ~B(? :: AD : BD. THEOREM XXIV. 284. Two triangles having an angle in each the same are to each other as the products of the sides including the equal angles. In the As ABC and DEC let the angle c be common. 0 To prove that A ABC : A DEC :: CA X CB : CD X CE....
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883 - 86 pages
...two adjoining sides of the one respectively equal to two adjoining sides of the other, and likewise an angle of the one equal to an angle of the other; the parallelograms are identically equal. [By Superposition.] COR. Two rectangles are equal, if two...
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Wentworth & Hill's Exercise Manuals: Geometry, Issue 3

George Albert Wentworth - 1884 - 264 pages
...radius of the circle. COMPARISON OP AREAS. 187. Theorem. The areas of two triangles having an angle of one equal to an angle of the other are to each other as the rectangles of the sides including the equal angles. 188. Theorem. Similar triangles are to each other...
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The Eclectic School Geometry

Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...; hence, it is also similar to DFE. Therefore, two triangles, etc. THEOREM XI. 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...
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The Elements of Plane Geometry ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...two adjoining sides of the one respectively equal to two adjoining' sides of the other, and likewise an angle of the one equal to an angle of the other ; the parallelograms are identically equal. Let ABCD, EFGH be two parallelograms having the angle ABC...
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The elements of plane geometry, Volume 1

Mathematical association - 1884 - 146 pages
...two adjoining: sides of the one respectively equal to two adjoining sides of the other, and likewise an ang:le of the one equal to an angle of the other ; the parallelograms are identically equal. Let ABCD, EFGH be two parallelograms having the angle ABC...
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The Common Sense of the Exact Sciences

William Kingdon Clifford - Mathematics - 1885 - 310 pages
...proposition about parallel lines.1 The first of these deductions will now show us that if two triangles have an angle of the one equal to an angle of the other and the sides containing these angles respectively equal, they must be equal in all particulars. For...
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 440 pages
...have the ZA common and the including sides proportional. .-. the A OAB and BAC are similar. " If two A have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar." 354 But the A OAB is isosceles. 221...
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 431 pages
...Z A'O'B', 442 and OA : OB = O'A' : O'B'. .-. the A OAB and O'A'B' are similar. "If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar." 354 /. AB : A'B' = OA : O'A' 349 = OH...
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Public Documents of Massachusetts, Volume 9

Massachusetts - Massachusetts - 1907 - 1342 pages
...is measured by one-half the difference of the intersected arcs. 3. Two triangles, having an angle of one equal to an angle of the other, are to each other as the product of the sides including the equal angles. Prove. 4. If the radius of a circle is 3v% what is...
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