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 and Trigonometry - Side 86av Adrien Marie Legendre - 1836 - 359 siderUten tilgangsbegrensning - Om denne boken
| Dalhousie University - 1888
...sides, the solids contained by the alternate segments of these lines are equal. 3. If two triangles **have an angle of the one equal to an angle of the other, and** have their areas proportional to the squares of the side* opposite these equal angles, they must be... | |
| Benjamin Franklin Finkel - 1888 - 481 sider
...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 - 386 sider
...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 - 1890 - 393 sider
...8, BC = 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 ZA-ZA, and... | |
| Euclid - 1890 - 400 sider
...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" ABC, AD... | |
| Edward Albert Bowser - 1890 - 393 sider
...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 - 271 sider
...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 one of the... | |
| 1893
...by a 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... | |
| Henry Martyn Taylor - 1893 - 504 sider
...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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