 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 Geometry - Page 65by Adrien Marie Legendre - 1841 - 235 pagesFull view - About this book
 | Benjamin Franklin Finkel - Mathematics - 1888 - 518 pages
...Two polygons that are similar to a third polygon ale similar to each other. 6. If two triangles have an angle of the one equal to an angle of the other, their areas are to each other as the rectangles of the sides including those angles. 7. The ratio of... | |
 | Euclid - Geometry - 1890 - 442 pages
...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 A" ABC, AD E be of equal area, AA... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...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 To prove A ABC similar... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...Euclid, about 300 nC (Prop. 47, Book I. Euclid). Proposition 8. Theorem. 375. The areas of 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. Hyp. Let ABC, ADE be the... | |
 | William Kingdon Clifford - Mathematics - 1891 - 312 pages
...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 if we take up... | |
 | William Chauvenet - 1893 - 340 pages
...A'B" 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... | |
 | Examinations - 1893 - 408 pages
...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 pages
...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 the parallelograms is equal to the ratio compounded of the ratios of the... | |
 | 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 - 390 pages
...the base of AABC 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 for Prop. XII., if AB,... | |
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