| George Albert Wentworth - Geometry - 1888 - 386 pages
...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 - Mathematics - 1888 - 481 pages
...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 - Geometry - 1888 - 386 pages
...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 - Geometry - 1890 - 400 pages
...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 - Geometry - 1890 - 393 pages
...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 - Geometry - 1890 - 393 pages
...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 - Mathematics - 1891 - 271 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... | |
| Examinations - 1893
...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 - 504 pages
...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
...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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