 | George Albert Wentworth - 1888 - Liczba stron: 272
...of the polygon. D AREAS OF POLYGONS. PROPOSITION VII. THEOREM. 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. Let the triangles ABC and... | |
 | Benjamin Franklin Finkel - 1888 - Liczba stron: 518
...5. 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... | |
 | George Albert Wentworth - 1888 - Liczba stron: 264
...proportional, but the homologous angles are not equal. PROPOSITION VII. THEOREM. V 326. If two triangles have an angle of the one equal to an angle of the othcr, and the including sides proportional, they are similar. In the triangles ABC and A'B'C ' , let... | |
 | Euclid - 1890 - Liczba stron: 442
...their 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"... | |
 | Edward Albert Bowser - 1890 - Liczba stron: 420
...10, find the lengths of the segments BD and CD. 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 A s ABC, A'B'C', let , AB __ AC... | |
 | Edward Albert Bowser - 1890 - Liczba stron: 418
...about 300 BC (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 - 1891 - Liczba stron: 312
...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... | |
 | 1893 - Liczba stron: 408
...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 - Liczba stron: 486
...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 - Liczba stron: 340
...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... | |
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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'... 
