 | William Kingdon Clifford - 1891 - 312 pagina’s
...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 respsctively equal, they must be equal in all particulars. For... | |
 | 1893 - 408 pagina’s
...tangent and a chord is measured by one half the intercepted arc. 1 2 5 Prove that 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. 16 6 Prove that the area... | |
 | Henry Martyn Taylor - 1893 - 486 pagina’s
...is to CD as EF to GH. (V. Prop. 16.) Wherefore, if the ratio ,fec. PROPOSITION 23. If two triangles have an angle of the one equal to an angle of the other, tlte ratio of the areas of the triangles is equal to the ratio compounded of the ratios of the sides... | |
 | William Chauvenet - 1893 - 340 pagina’s
...hence AD BC 'AT? A'D' B'C' and we have ARC _ = 'AT? A'B'O' EXERCISE. Theorem. — 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. Suggestion. Let ADE and... | |
 | George Albert Wentworth, George Anthony Hill - 1894 - 150 pagina’s
...circumferences at B and C respectively ; show that BA is perpendicular to AC. 4. Assuming that 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, prove that the bisector... | |
 | Henry Martyn Taylor - 1895 - 708 pagina’s
...the ratios AB to DE and BC to EF. Wherefore, if two triangles &c. COROLLARY. If two parallelograms have an angle of the one equal to an angle of the other, the ratio of the areas of th« parallelograms is equal to the ratio compounded of the ratios of the... | |
 | John Macnie - 1895 - 386 pagina’s
...at the base of A ABC in Prop XI. are equal, how is the proposition modified ? 381. If two triangles have an angle of the one equal to an angle of the other, and the sides about another angle proportional, are they necessarily similar ? 382. In the diagram... | |
 | George Albert Wentworth - 1895 - 458 pagina’s
...of these figures will be the area of the polygon. B PROPOSITION VII. THEOREM. 374. The areas of two triangles which have an angle of the one equal to an angle of tlie other are to each other as the products of the sides including the equal angles. Let the triangles... | |
 | George Albert Wentworth - 1896 - 68 pagina’s
...The area of a trapezoid is equal to the product of the median by the altitude. 374. 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. 375. The areas of two similar... | |
 | Joe Garner Estill - 1896 - 186 pagina’s
...circumferences at B and C respectively ; show that BA is perpendicular to A C. 4. Assuming that 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, prove that the bisector... | |
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Assuming that 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... 
