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'... An Elementary Treatise on Plane and Solid Geometry - Page 146by Benjamin Peirce - 1871 - 150 pagesFull view - About this book
| Lewis Carroll - Geometry - 1885 - 318 pages
...have two adjacent sides of the one respectively equal to two adjacent sides of the other, and likewise **an angle of the one equal to an angle of the other** ; the Parallelograms are identically equal.' This might be a useful exercise to set ; but really it... | |
| William Chauvenet - Geometry - 1887 - 331 pages
...B'C' A'B" hence AD BC A'D' X B'C' and we have ABC A' B' C' 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... | |
| Dalhousie University - 1888
...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
...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 - 386 pages
...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 - 274 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 - 400 pages
...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 - 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 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
...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... | |
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