| George Albert Wentworth - Geometry - 1888 - 274 pages
...proportional, but the homologous angles are not equal. PROPOSITION VII. THEOREM. 326. If two triangles **have an angle of the one equal to an angle of the other,** and the including sides proportional, they are similar. In the triangles ABC and A'B'C', let ZA=ZA',... | |
| 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... | |
| Edward Albert Bowser - Geometry - 1890 - 418 pages
...= 12, and AC — 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... | |
| 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... | |
| 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... | |
| Examinations - 1893
...tangent and a 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 of a regular... | |
| 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 ABC be... | |
| 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... | |
| 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 of an angle... | |
| John Macnie - Geometry - 1895 - 392 pages
...QED (232"') SCHOLIUM. The theorem may be expressed also under the form : The areas of triangles that **have an angle of the one equal to an angle of the other, are** as the products of the sides about those angles. PROPOSITION IX. THEOREM. 342. Similar triangles are... | |
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