 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'...  An Elementary Treatise on Plane and Solid Geometry - Page 146by Benjamin Peirce - 1871 - 150 pagesFull view - About this book
 | Henry Martyn Taylor - 1893 - 486 pages
...therefore AB 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... | |
 | Examinations - 1893 - 408 pages
...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... | |
 | William Chauvenet - 1893 - 340 pages
...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 - Geometry - 1894 - 150 pages
...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... | |
 | John Macnie - Geometry - 1895 - 386 pages
...same diagram, show that rect. A E- (AB+ EBy^T? — Elf. PROPOSITION VIII. THEOREM. 341. Triangles that have an angle of the one equal to an angle of the other, are to each other as the rectangles contained by the sides including those angles. AD c A, D, a' Given:... | |
 | Henry Martyn Taylor - Euclid's Elements - 1895 - 708 pages
...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... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...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... | |
 | Joe Garner Estill - Geometry - 1896 - 168 pages
...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... | |
 | Joe Garner Estill - 1896 - 186 pages
...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... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...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... | |
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