 | Trinity College (Dublin, Ireland) - 1907 - 536 pages
...and CB in points D and E respectively, so that OA : AD = CB : BE, prove that DE is parallel to AB. 8. If two triangles have an angle of the one equal to an angle of the other and the sides about the equal angles reciprocally proportional, prove the triangles equal in area. 9. Given any two... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 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 sides... | |
 | Great Britain. Education Department. Department of Science and Art - 1908 - 328 pages
...triangle and of half its area, from whose sides the given circle shall cut off equal chords. (25) 43. If two triangles have an angle of the one equal to an angle of the other and the sides about those angles proportional, show that the triangles are equiangular to one another. Find a point... | |
 | William Ernst Paterson - Algebra - 1908 - 614 pages
...are equiangular, the ratios of corresponding aides are equal. Theorem III. If two triangles have one angle of the one equal to an angle of the other and the aides about the equal angles proportional, then' the triangles are equiangular. 237. Theorem I leads... | |
 | Michigan. Department of Public Instruction - Education - 1909 - 356 pages
...through a point in the circumference of a circle two chords are drawn, 4. (a) Two triangles having 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) To trisect a right angle.... | |
 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...respectively, to two angles of the other. PROPOSITION XVIII. THEOREM. 368. Two triangles are similar if they have an angle of the one equal to an angle of the other and the including sides proportional. EF Given As ABC and DBF in which XA = XD, and — = — . DE DF To prove... | |
 | 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'... | |
 | 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... | |
 | 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... | |
 | 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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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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'... 
