 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 = Z A', and let AB : A'B' = AC : A'C'. To prove that the A ABC and A'B'C' are similar....  A Text-book of Geometry - Page 148by George Albert Wentworth - 1889 - 242 pagesFull view - About this book
 | William Chauvenet, William Elwood Byerly - 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 - 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... | |
 | 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,... | |
 | 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,... | |
 | Webster Wells - Algebra - 1890 - 604 pages
...the triangles EOG and COD ; for, by Geometry, two triangles are similar when they have an angle of one equal to an angle of the other, and the including sides proportional. Then the figure OFEG is similar to OBDC, and hence OFEG is a parallelogram. Therefore OE represents... | |
 | 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... | |
 | 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... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 246 pages
...each other as the products of their bases by their altitudes. 410. 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. 412. The areas of two similar... | |
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