| Dalhousie University - 1888 - 212 pages
...parallel to the 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 - Mathematics - 1888 - 518 pages
...circle; and conversely. 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 - 264 pages
...homologous sides are 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... | |
| George Albert Wentworth - Geometry - 1888 - 272 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... | |
| Euclid - Geometry - 1890 - 442 pages
...the other, have 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 - Geometry - 1890 - 420 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 ZA-ZA, and... | |
| Edward Albert Bowser - Geometry - 1890 - 418 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 - 312 pages
...is the famous 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... | |
| Henry Martyn Taylor - 1893 - 486 pages
...GSTUH, therefore AB 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... | |
| Examinations - 1893 - 392 pages
...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... | |
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