| Trinity College (Dublin, Ireland) - 1907 - 534 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 - 350 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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