 | Euclid - 1890 - 442 sider
...sides about the equal angles reciprocally proportional : (/3) and conversely, 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, the triangles have the same area. Let... | |
 | Edward Albert Bowser - 1890 - 414 sider
...A'B'C' is similar to the A ABC. QED EXERCISE. Proposition 1 8. Theorem. 314. Two triangles which have an angle of the one equal to an angle of the other, and the sides about these angles proportional, are similar. Hyp. In the AS ABC, A'B'C', let AB AC nv... | |
 | William Kingdon Clifford - 1891 - 312 sider
...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... | |
 | William Chauvenet - 1893 - 340 sider
...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... | |
 | 1893 - 408 sider
...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 sider
...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... | |
 | George Albert Wentworth, George Anthony Hill - 1894 - 150 sider
...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 sider
...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 sides... | |
 | John Macnie - 1895 - 386 sider
...angle B, and angle B to angle C, then the figure is a parallelogram. 73. If two parallelograms have an angle of the one equal to an angle of the other, they are mutually equiangular. 74. A parallelogram whose diagonals are equal is a rectangle. 75. A... | |
 | Joe Garner Estill - 1896 - 214 sider
...whatever direction the chord is drawn. 6. Prove the ratio between the areas of two triangles which have an angle of the one equal to an angle of the other. Define area. 7. Define a regular polygon and prove that two regular polygons of the same number of... | |
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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... 
