 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw...  Elements of Plane Geometry: For the Use of Schools - Page 71by Nicholas Tillinghast - 1844 - 96 pagesFull view - About this book
 | 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
...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... | |
 | George Albert Wentworth - Geometry - 1895 - 458 pages
...areas 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... | |
 | 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... | |
 | 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:... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...Cor. 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... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...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... | |
 | Joe Garner Estill - 1896 - 186 pages
...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... | |
 | Joe Garner Estill - 1896 - 214 pages
...segments is constant in 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 - Geometry - 1896 - 168 pages
...by twice the square on the median to that side. Amherst College, June, 1896. 1. Two triangles having an angle of the one equal to an angle of the other, and the including sides proportional are similar. 2. Inscribe a circle in a given triangle. 3. (1) When are... | |
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