 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. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB...  Solid Geometry - Page 250by George Albert Wentworth - 1902 - 218 pagesFull view - About this book
 | 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.... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...is a mean proportional between the segments of the other. 51. Two parallelograms are similar if they have an angle of the one equal to an angle of the other and the including sides proportional. 52. Two rectangles are similar if two adjoining pairs of homologous... | |
 | 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... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...THEOREM. Two triangular pyramids (tetrahedrons) having a trihedral angle of one equal to a trihedral angle of the other are to each other as the products of the three edges including the equal trihedral angles. Given : Triangular pyramids S-ABC, S—PQR; having... | |
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